List of Stephen Yau's Main Publications on Pure Math
October 30, 2024

1.        On the Nakai Conjecture for some singularities (with Zida Xiao, Qiwei Zhu and Huaiqing Zuo), to appear, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2024.

2.        On T-maps and ideals of antiderivatives of hypersurface singularities (with Quan Shi and Huaiqing Zuo), to appear, Izvestiya: Mathematics, 2024.

3.        Hodge moduli algebras and complete invariants of singularities (with Guorui Ma, Yang Wang, and Huaiqing Zuo), Asian Journal of Mathematics, Vol. 28, No. 1 (2024), 001-046.

4.        A characterization and solvability of quasihomogeneous singularities (with Guorui Ma, Qiwei Zhu and Huaiqing Zuo), Pacific Journal of Mathematics, Vol. 329, No. 1 (2024), 121-146.

5.        On variation of complex structures and variation of new Lie algebras arising from singularities (with Bingyi Chen, Naveed Hussain and Huaiqing Zuo), Proceedings of the 8th International Consortium of Chinese Mathematicians, 2019, Beijing, China, Vol. 1 (2024), 731-743.

6.        Bergman functions and the equivalence problem of singular domains (with Bingyi Chen), Communications in Analysis and Geometry, Vol. 31, No. 2 (2023), 449-483.

7.        Classification of weighted dual graphs consisting of -2 curves and exactly one -3-curve (with Qiwei Zhu and Huaiqing Zuo), Izvestiya: Mathematics, Vol. 87, No. 5 (2023), 1078-1116.

8.        A criteria for classification of weighted dual graphs of singularities and its application (with Qiwei Zhu and Huaiqing Zuo), Asian Journal of Mathematics, Vol. 27, No. 2 (2023), 261-300.

9.        On derivation Lie algebras of isolated complete intersection singularities (with Naveed Hussain and Huaiqing Zuo), Letters in Mathematical Physics, Vol. 113:99 (2023), 1-34.

10.    Nonexistence of negative weight derivations of the local k-th Hessian algebras associated to isolated singularities (with Guorui Ma and Huaiqing Zuo), Pacific Journal of Mathematics, Vol. 323, No. 1 (2023), 129-172.

11.    Derivations of local k-th Hessian algebras of singularities (with Naveed Hussain and Huaiqing Zuo), Rocky Mountain Journal of Mathematics, Vol. 53, No. 1 (2023), 65-87.

12.    k-th Milnor Numbers and k-th Tjurina Numbers of Weighted Homogeneous Singularities (with Naveed Hussain*, Zhiwen Liu* and Huaiqing Zuo), Geometriae Dedicata, Vol. 217, No. 34 (2023), 1-35.

13.    k-th singular locus moduli algebras of singularities and their derivation Lie algebras (with Guorui Ma and Huaiqing Zuo), Journal of Mathematical Physics, Vol. 64:031701 (2023), 1-13

14.    Higher Nash blow-up local algebras of singularities and its derivation Lie algebras (with Naveed Hussain, Guorui Ma and Huaiqing Zuo), Journal of Algebra, Vol. 618 (2023), 165-194.

15.    Complex structures of a twenty dimensional family of Calabi-Yau 3-folds (with Chuangqiang Hu and Huaiqing Zuo), Communications in Analysis and Geometry, Vol. 30, No. 8 (2022), 1825-1831.

16.    Non-existence of negative weight derivations of the local 1-st Hessian algebra of singularities (with Shuanghe Fan and Huaiqing Zuo), Asian Journal of Mathematics, Vol. 26, No. 3 (2022), 289-372.

17.    On Derivation Lie Algebras of Singularities and Torelli-Type Theorems (with Huaiqing Zuo), Notices of the ICCM, Vol. 10, No. 2 (2022), 30-39.

18.    Generalized Cartan matrices associated to k-th Yau algebras of singularities and Characterization theorem (with Naveed Hussain and Huaiqing Zuo), Algebras and Representation Theory, Vol. 25 (2022), 1461-492.

19.    An inequality conjecture and a weak Torelli-type theorem for isolated complete intersection singularities (with Naveed Hussain and Huaiqing Zuo), Journal of Geometry and Physics, Vol. 178 (2022), 104542, 1-19.

20.    New k-th Yau Algebras of Isolated Hypersurface Singularities and Weak Torelli-Type Theorem (with Naveed Hussain and Huaiqing Zuo), Mathematical Research Letters, Vol. 29, No. 2 (2022), 455-486.

21.    Classification of the nilradical of k-th Yau algebras arising from singularities (with Naveed Hussain and Huaiqing Zuo), Pure and Applied Mathematics Quarterly, Vol. 18, No. 3 (2022), 835-862.

22.    Kohn-Rossi Cohomology and Complex Plateau Problem (with Xiankui Meng), Pure and Applied Mathematics Quarterly, Vol. 18, No. 2 (2022), 683-718.

23.    Geometric nilpotent Lie algebras and zero-dimensional simple complete intersection singularities (with Naveed Hussain and Huaiqing Zuo), Forum Mathematicum, Vol. 34, No. 2 (2022), 323-345.

24.    Rigidity of CR morphisms (with Xiankui Meng), Pacific Journal of Mathematics, Vol. 316, No. 1 (2022), 207-216.

25.    ON THE DIMENSION OF A NEW CLASS OF DERIVATION LIE ALGEBRAS ASSOCIATED TO SINGULARITIES (with Naveed Hussain and Huaiqing Zuo), Mathematics, Vol. 9, No. 14 (2021), 1-15.

26.    Derivation Lie Algebras of New k-TH Local Algebras of Isolated Hypersurface Singularities (with Naveed Hussain and Huaiqing Zuo), Pacific Journal of Mathematics, Vol. 314, No. 2 (2021), 311-331.

27.    Inequality conjectures on derivations of local k-th Hessain algebras associated to isolated hypersurface singularities (with Naveed Hussain and Huaiqing Zuo), Mathematische Zeitschrift, Vol. 298 (2021), 1813-1829.

28.    On the Generalized Cartan Matrices Arising from k-th Yau Algebras of Isolated Hypersurface Singularities (with Naveed Hussain and Huaiqing Zuo), Algebras and Representation Theory, Vol. 24 (2021), 1101-1124.

29.    On two inequality conjectures for the k-th Yau numbers of isolated hypersurface singularities (with Naveed Hussain, and Huaiqing Zuo), Geometriae Dedicata, Vol. 212 (2021), 57-71.

30.    kth Yau number of isolated hypersurface singularities and an inequality conjecture (with Naveed Hussain and Huaiqing Zuo), Journal of the Australian Mathematical Society, Vol. 110 (2021), 94-118.

31.    4D N = 2 SCFT and singularity theory part IV: isolated rational Gorenstein non-complete intersection singularities with at least one-dimensional deformation and nontrivial T2 (with Bingyi Chen, Shing-Tung Yau and Huaiqing Zuo), Mathematical Research Letters, Vol. 28, No 1 (2021), 1-23.

32.    Recent results on k-th Yau algebras over simple elliptic singularities ~E6 (with Chuangqiang Hu and Huaiqing Zuo), Surveys in Differential Geometry, Vol. 23 (2020), 213-240.

33.    On the non-existence of negative weight derivations of the new moduli algebras of singularities (with Guorui Ma and Huaiqing Zuo), Journal of Algebra, Vol. 564 (2020), 199-246.

34.    Variation of complex structures and variation of Lie algebras II: new Lie algebras arising from singularities (with Bingyi Chen, Naveed Hussain and Huaiqing Zuo), Journal of Differential Geometry, Vol. 115, No. 3 (2020), 437-473.

35.    The Nonexistence of Negative Weight Derivations on Positive Dimensional Isolated Singularities: Generalized Wahl Conjecture (with Bingyi Chen, Hao Chen and Huaiqing Zuo), Journal of Differential Geometry, Vol. 115, No. 2 (2020), 195-224.

36.    On classification of toric surface codes of dimension seven (with Naveed Hussain, Xue Luo, Mingyi Zhang and Huaiqing Zuo), Communications in Analysis and Geometry, Vol. 28, No. 2 (2020), 263-319.

37.    Generalized Cartan matrices arising from new derivation Lie algebras of isolated hypersurface singularities (with Naveed Hussain and Huaiqing Zuo), Pacific Journal of Mathematics, Vol. 305, No. 1 (2020), 189-217.

38.    On the new k-th Yau algebras of isolated hypersurface singularities (with Naveed Hussain and Huaiqing Zuo), Mathematische Zeitschrift, Vol. 294 (2020), 331-358.

39.    Complete Weight Distributions and MacWilliams Identities for Asymmetric Quantum Codes (with Chuangqiang Hu, and Shudi Yang), IEEE Access, Vol. 7 (2019), 68404- 68414.

40.    Non-existence of negative weight derivations on positively graded Artinian algebras (with Hao Chen and Huaiqing Zuo), Transactions of the American Mathematical Society, Vol. 372, No. 4 (2019), 2493-2535.

41.    Kohn-Rossi cohomology and nonexistence of CR morphisms between compact strongly pseudoconvex CR manifolds (with Huaiqing Zuo), Journal of Differential Geometry, Vol. 111 (2019), 567-580.

42.    4d N = 2 SCFT and singularity theory Part III: Rigid singularity (with Bingyi Chen, Dan Xie, Shing-Tung Yau and Huaiqing Zuo), Advances in Theoretical and Mathematical Physics, Vol. 22, No. 8 (2018), 1885-1905.

43.    On the derivation Lie algebras fewnomial singularities (with Naveed Hussain and Huaiqing Zuo), Bulletin of the Australian Mathematical Society, Vol. 98 (2018), 77-88.

44.    Sharp Upper Estimate of Geometric Genus and Coordinate-free Characterization of Isolated Homogeneous Hypersurface Singularities (with Ke-Pao Lin, S. Raghuvanshi and Huaiqing Zuo), Asian Journal of Mathematics, Vol. 22, No. 4 (2018), 599-646.

45.    A sharp lower bound for the geometric genus and Zariski multiplicity question (with Huaiqing Zuo), Mathematische Zeitschrift, Vol. 289 (2018), 1299-1310.

46.    4d N = 2 SCFT from Complete Intersection Singularity (with Yifan Wang, Dan Xie, and Shing-Tung Yau), Advances in Theoretical and Mathematical Physics, Vol. 21, No. 3 (2017), 801-855.

47.    Thom-Sebastiani properties of Kohn-Rossi cohomology of compact connected strongly pseudoconvex CR manifolds (with Huaiqing Zuo), Science China Mathematics, Vol. 60, No. 6 (2017), 1129-1136.

48.    4d N=2 SCFT and singularity theory Part II: Complete intersection (with Bingyi Chen, Dan Xie, Shing-Tung Yau and Huaiqing Zuo), Advances in Theoretical and Mathematical Physics, Vol. 21, No. 1 (2017), 121-145.

49.    On the Sharp Polynomial Upper Estimate Conjecture in Eight-Dimensional Simplex (with Ke-Pao Lin, Andrew Yang and Huaiqing Zuo), Pure and Applied Mathematics Quarterly, Vol. 12, No. 3 (2016), 353-398.

50.    A Sharp upper estimate conjecture for the Yau number of a weighted homogeneous isolated hypersurface singularity (with Huai Qing Zuo), Pure and Applied Mathematics Quarterly, Vol. 12, No. 1 (2016), 165-181.

51.    Derivations of the moduli algebras of weighted homogeneous hypersurface singularities (with Huaiqing Zuo), Journal of Algebra, Vol. 457 (2016), 18-25.

52.    A sharp estimate of positive integral points in 6-dimensional polyhedra and a sharp estimate of smooth numbers (with Andrew Liang and Huaiqing Zuo), SCIENCE CHINA Mathematics, Vol. 59, No. 3 (2016), 425-444.

53.    On the polynomial sharp upper estimate conjecture in 7-dimensional simplex (with Beihui Yuan and Huaiqing Zuo), Journal of Number Theory, Vol. 160 (2016), 254-286.

54.    On higher dimensional complex Plateau problem (with Rong Du and Yun Gao), Mathematische Zeitschrift, Vol. 282 (2016), 389-403.

55.    Topological Classification of Simplest Gorenstein Non-complete Intersection Singularities of Dimension 2 (with Mingyi Zhang and Huaiqing Zuo), Asian Journal of Mathematics, Vol. 19, No. 4 (2015), 651-792.

56.    Plurigenera of compact connected strongly pseudoconvex CR manifolds (with Ke-Pao Lin and Huaiqing Zuo), Science China Mathematics, Vol. 58, No. 3 (2015), 525-530.

57.    Complete characterization of isolated homogeneous hypersurface singularities (with Huaiqing Zuo), Pacific Journal of Mathematics, Vol. 273, No. 1 (2015), 213-224.

58.    A sharp polynomial estimate of positive integral points in a 4-dimensional tetrahedron and a sharp estimate of the Dickman-de Bruijn function (with Xue Luo and Huaiqing Zuo), Mathematische Nachrichten, Vol. 288, No. 1 (2015), 61-75.

59.    On a number-theoretic conjecture on positive integral points in a 5-dimensional tetrahedron and a sharp estimate of the Dickman-De Bruijn function (with Ke-Pao Lin, Xue Luo, and Huaiqing Zuo), Journal of the European Mathematical Society, Vol. 16 (2014), 1937-1966.

60.    On variance of exponents for isolated surface singularities with modality ≤ 2 (with Huaiqing Zuo), Science China Mathematics, Vol. 57, No. 1 (2014), 31-41.

61.    Several splitting criteria for vector bundles and reflexive sheaves (with Fei Ye), Pacific Journal of Mathematics, Vol. 266, No. 2 (2013), 449-456.

62.    Nonconstant CR morphisms between compact strongly pseudoconvex CR manifolds and etale covering between resolutions of isolated singularities (with Yu-Chao Tu and Huaiqing Zuo), J. Differential Geometry, Vol. 95 (2013), 337-354.

63.    Characterization of isolated complete intersection singularities with C*-action of dimension n≥2 by means of geometric genus and irregularity (with Huaiqing Zuo), Communications in Analysis and Geometry, Vol. 21, No. 3 (2013), 509-526.

64.    Sharp polynomial estimate of integral points in right-angled simplices (with Linda Zhao), Journal of Number Theory, Vol. 133, No. 2 (2013), 398-425.

65.    Lower estimate of milnor number and characterization of isolated homogeneous hypersurface singularities (with Huaiqing Zuo), Pacific J. math., Vol. 260, No. 1 (2012), 245-255.

66.    Kohn-Rossi cohomology and its application to the complex plateau problem, III (with Rong Du), J. Differential Geometry, Vol. 90 (2012), 251-266.

67.    New invariants for complex manifolds and isolated singularities (with Rong Du and Hing Sun Luk), Communications in Analysis and Geometry, Vol. 19, No. 5 (2011), 991-1021.

68.    Coordinate-free characterization of homogeneous polynomials with isolated singularities (with Irene Chen, Ke-Pao Lin, and Huaiqing Zuo), Communications in analysis and geometry, Vol. 19, No. 4 (2011), 661-704.

69.    A note on the topology of the complements of fiber-type line arrangements in CP2 (with Shengli Tan and Fei Ye), Pacific Journal of Mathematics, Vol. 251, No.1 (2011), 207-218.

70.    Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds, Journal of European Mathematical Society, Vol. 13 (2011), 175-184.

71.    Explicit Construction of Moduli Space of Bounded Complete Reinhardt Domains in Cn (with Rong Du and Yun Gao), Communications in Analysis and Geometry, Vol. 18, No. 3 (2010), 601-626.

72.    Lojasiewicz inequality for weighted homogeneous polynomial with isolated singularity (with Shengli Tan and Huaiqing Zuo), Proceeding of the Amer. Math. Soc. Vol. 138, No. 11 (2010), 3975-3984.

73.    Local holomorphic De Rham cohomology (with Rong Du), Communications in Analysis and Geometry, Vol. 18, No. 2 (2010), 365-374.

74.    The second pluri-genus of smoothable Gorenstein surface singularities (with Rong Du), Science China Mathematics, Vol. 53, No. 3 (2010), 635-639.

75.    Spherical extension property no longer true for domains in algebraic variety with isolated singularity (with Shanyu Ji and Cheng Zhan), Science China Mathematics, Vol. 53, No.2 (2010), 257-260.

76.    Diffeomorphic types of complements of nice point arrangements in CPl (with Fei YE), Science in China, Series A Mathematics, Vol. 52, No. 12 (2009), 2774-2791.

77.    Classification of gradient space of dimension 8 by a reducible sl(2,C) action (with Yung Yu and Huaiqing Zuo), Science in China, Series A Mathematics, Vol. 52, No. 12 (2009), 2792-2828.

78.    Some Primitive Linear Groups of Prime degree (with Ming-chang Kang, Ji-ping Zhang, Jian-yi Shi and Yung Yu), Journal of Mathematical Society of Japan, Vol. 61, No. 4 (2009), 1013-1070.

79.    Higher order Bergman functions and explicit construction of moduli space for complete Reinhardt domains (with Rong DU), Journal of Differential Geometry, Vol. 82 (2009), 567-610.

80.    On formulas of Dedekind sums and the number of lattice points in tetrahedra (with Letian Zhang), Journal of Number Theory, Vol. 129 (2009), 1931-1955.

81.    Classification of weight dual graphs with only complete intersection singularities structures (with Fan Chung Graham and Y.-J. Xu), Trans. Amer. Math. Soc, Vol. 361, No. 7 (2009), 3535-3596.

82.    The diffeomorphic types of the complements of arrangements in CP3 II (with Shaobo Wang), Science in China, Series A: Mathematics, Vol. 51, No. 4, (2008), 785-802.

83.    Kohn-Rossi cohomology and its application to the complex plateau problem, II (with H.S. Luk), Journal of Differential Geometry, Vol. 77, No. 1 (2007), 135-148.

84.    the Diffeomorphic types of the complements of arrangements in CP3 I: point arrangements (with Shaobo Wang), Journal of Math. Soc. of Japan, Vol. 59, No.2 (2007), 423-447.

85.    On the GLY conjecture of upper estimate of positive integral points in real right-angled simplices (with Xuejun Wang), Journal of Number Theory, Vol. 122, No. 1 (2007), 184-210.

86.    An upper estimate of integral points in real simplices with application to singularity theory (with Letian Zhang), Math. Research Letter, Vol. 13, No. 6 (2006), 911-922.

87.    Characterization of isolated homogeneous hypersurface singularities in C4 (with Kepao Lin and Zhanhan Tu), Science in China. Series A: Mathematics, Vol. 49, No. 11 (2006), 1576-1592.

88.    A remark on lower bound of Milnor number and characterization of homogeneous hypersurface singularities (with Ke-Pao Lin, Xi Wu and Hing-Sun Luk), Communications in Analysis and Geometry, Vol. 14, No. 4 (2006), 625-632.

89.    On a CR family of compact strongly pseudoconvex CR manifolds (with X. Huang and H.S. Luk), Journal of Differential Geometry, Vol. 72, No. 3 (2006), 353-379.

90.    Complete invariant of a family of strongly pseudoconvex domains in A1-singularity: Bergman function (with Hing Sun Luk and Weitian Zang), Contemporary Math., AMS, Vol. 400 (2006), 161-171.

91.    General Finite type IFS and M-matrix (with Ning Jin), Communication in Analysis and Geometry, Vol. 13, No. 4 (2005), 821-843.

92.    Rigidity of differentiable structure for new class of line arrangements (with Shaobo Wang), Communications in Analysis and Geometry, Vol. 13, No. 5 (2005), 1057-1075.

93.    Classification of 3-dimensional isolated rational hypersurface singularities with C*-action, (with Yung Yu), Rocky Mountain Journal of Mathematics, Vol. 35, Issue 4 (2005), 1795-1802.

94.    Global invariants for strongly pseudoconvex varieties with isolated singularities: Bergman functions, Mathematical Research Letter, Vol. 11 (2004), 809-832.

95.    Classification of affine varieties being cones over nonsingular projective varieties: hypersurface case (with Ke-Pao Lin), Communications in Analysis and Geometry. Vol. 12, No. 5 (2004), 1201-1219.

96.    Lower estimate of multiplicity of isolated complete intersection singularities with applications in weakly elliptic singularities (with Yijing Xu), Mathematical Research Letter, Vol. 11 (2004), 59-71.

97.    Hausdorff dimension of invariant c-vector of M-matrix and self-affine fractals (with Ning Jin), Asian Journal of Mathematics, Vol. 8, No. 2 (2004), 259-286.

98.    Holomorphic De-Rham cohomology of strongly pseudoconvex CR manifolds with holomorphic S1-actions (with Hing Sun Luk), Journal of Differential Geometry, Vol. 63 (2003), 155-170.

99.    Some remarks on the local moduli of tangent bundles over complex surfaces (with W.S. Cheung and B. Wong), Amer. J. Math., Vol. 125 (2003), 1029-1035.

100.              Punctured local holomorphic de Rham cohomology (with Xiaojun Huang and Hing Sun Luk), Journal of the Math. Soc. of Japan, Vol. 55, No. 3 (2003), 633-640.

101.              Counting the number of integral points in general n-dimensional Tetrahedra and Bernoulli polynomials (with K.P. Lin), Canadian Mathematical Bulletin, Vol. 46, No. 2 (2003), 229-241.

102.              Algebraic classification of rational CR-structures on topological 5-sphere with transversal holomorphic S1-action in C4 (with Yung Yu), Math. Nachr., Vol. 246-247 (2002), 207-233.

103.              Analysis for a sharp polynomial upper estimate of the number of positive integral points in a 4-dimensional tetrahedron (with Ke-Pao Lin), J. Reine Angew. Math., Vol. 547 (2002), 191-205.

104.              A sharp upper estimate of the number of integral points in a 5-dimensional Tetrahedra (with Ke-Pao Lin), Journal of Number Theory, Vol. 93 (2002), 207-234.

105.              Bergman kernels on resolutions of isolated singularities (with H.S. Luk and L.Y. Yeh), Mathematical Research Letters, Vol. 8 (2001), 303-319.

106.              An example of a real analytic strongly pseudoconvex hypersurfaces which is not holomorphically equivalent to any algebraic hypersurfaces (with Xiaojun Huang and Shanyu Ji), Arkiv for Mathematik, Vol. 39 (2001), 75-93.

107.              Simple geometric characterization of supersolvable arrangements (with Tan Jiang and Larn-Ying Yeh), Rocky Mountain Journal of Mathematics, Vol. 31, No. 1 (2001), 303-312.

108.              Algebraic determination of isomorphism classes of the moduli algebras of E6 singularities (with Hao Chen, and Craig Seeley), Math. Ann., Vol. 318 (2000), 637-666.

109.              Moduli and Modular groups of a class of Calabi-Yau n-dimensional manifolds, n≥3 (with Hao Chen), Journal of Differential Geometry, Vol.54, No. 1 (1999), 1-12.

110.              Counterexample to boundary regularity of a strongly pseudoconvex CR submanifold: An addendum to the paper of Harvey-Lawson (with Hing Sun Luk), Annals of Mathematics, Vol. 148 (1998), 1153-1154.

111.              Intersection lattices and topological structures of complements of arrangements in CP2 (with Tan Jiang), Ann. Scuola Norm. Sup. Pisa Cl. Sci (4), Vol. XXVI (1998), 357-381.

112.              Explicit construction of graph invariant for strongly pseudo-convex compact 3-dimensional rational CR manifolds (with Hing-Sun Luk), Compositio Mathematica, Vol. 114 (1998), 77-111.

113.              A sharp estimate of the number of integral points in a 4-dimensimal tetrahedron (with Yi-Jing Xu), Journal fur die reine und ange wandte Mathematik, Vol. 473 (1996), 1-23.

114.              Microlocal characterization of quasi-homogeneous singularities (with Yijing Xu), Amer. J. Math, Vol. 118 (1996), 389-399.

115.              Invariant Kohn-Rossi cohomology and obstruction to embedding of compact real (2n-1)-dimensional CR manifolds in CN (with H.-S. Luk), Journal of the Mathematical Society of Japan, Vol. 48 (1996), 61-68.

116.              Nonexistence of Negative Weight Derivation of Moduli Algebras of Weighted Homogeneous Singularities (with Hao Chen and Yi-Jing Xu), Journal of Algebra, Vol. 172 (1995), 243-254.

117.              Algebraic classification and obstructions of embedding of strongly Pseudoconvex compact 3- dimensional CR manifolds in C3 (with Hing Sun Luk and Yung Yu), Math. Nachr., Vol. 170 (1994), 183-200.

118.              Diffeomorphic types of the complements of arrangements of hyperplanes (with Tan Jiang), Composito Mathematica, Vol. 92, No. 2 (1994), 133-155.

119.              Cohomology and Splitting Criterion for holomorphic vector bundles on CPn (with Hing Sun Luk), Math. Nachr., Vol. 161 (1993), 223-238.

120.              Gorenstein quotient singularities in dimension three (with Yung Yu), Mem. Amer. Math. Soc., Vol. 105, No. 105 (1993), 1-81.

121.              Durfee conjecture and coordinate free characterization of homogeneous singularities (with Yi-Jing Xu), Journal of Differential Geometry, Vol. 37 (1993), 375-396.

122.              A Sharp estimate of the number of integral points in a tetrahedron (with Yi-Jing Xu), Journal fur die reine und angewandte Mathematik, Vol. 423 (1992), 199-219.

123.              Classification of gradient space as sl(2,C)-module I (with J. Sampson and Yung Yu), Amer. J. Math., Vol. 114 (1992), 1147-1161.

124.              Solvability of Lie algebras arising from isolated singularities and nonisolatedness of singularities defined by sl(2,C) invariant polynomials, Amer. J. Math., Vol. 113 (1991), 773-778.

125.              Regularity for the Harvey-Lawson solutions to the complex Plateau problem, J. Differential Geom., Vol. 34 (1991), 425-429.

126.              A remark on moduli of complex hypersurface, Amer. J. Math., Vol. 113 (1990), 287-292.

127.              An obstruction for smoothing of Gorenstein surface singularities (with A. Libgober), Comment. Math. Helv., Vol. 65 (1990), 413-433.

128.              Equivalence between isolated hypersurface singularities (with Max Benson), Math. Ann., Vol. 287 (1990), 107-134.

129.              Variation of complex structures and variation of Lie algebras (with Craig Seeley), Invent. Math., Vol. 99 (1990), 545-565.

130.              the Multiplicity of isolated two-dimensional hypersurface singularities: Zariski problem, Amer. J. Math., Vol. 111 (1989), 753-767.

131.              Classification of topological types of isolated quasi-homogeneous two-dimensional hypersurface singularities (with Yijing Xu), Mancripta Math., Vol. 64 (1989), 445-469.

132.              Classification of Jacobian ideals invariant by sl(2,C) actions, Mem. Amer. Math. Soc., Vol. 72 (1988), 1-180.

133.              Holomorphic symmetries (with Blaine Lawson), Ann. Sci. Ecole Norm. Sup. 4e series, t., Vol. 20 (1987), 557-577.

134.              Lie algebras and their representations arising from isolated singularities: Computer method in calculating the Lie algebra and their cohomology (with Max Benson), Adv. Stud. Pure Math. 8, Complex Analytic Singularities (1986), 3-58.

135.              Singularities defined by sl(2,C) invariant polynomials and solvability of Lie algebras arising from isolated singularities, Amer. J. Math., Vol. 108 (1986), 1215-1239.

136.              Solvable Lie algebras and generalized Cartan Matrices arising from isolated singularities, Math. Z., Vol. 191 (1986), 489-506.

137.              An estimate of the gap of the first two eigenvalues in the Schrodinger operator (with I.M. Singer, Bun Wong and Shing-Tung Yau), Ann. Scuola Norm. Sup., Pisa, Classe di Scienze, Serie IV, Vol. XII, No. 2 (1985), 319-333.

138.              Continuous family of finite-dimensional representations of a solvable Lie algebra arising from singularities, Proc. Nat. Acad. Sci. U.S.A., Vol. 80 (1983), 7694-7696.

139.              Various numerical invariants for isolated singularities, Amer. J. Math., Vol. 104, No. 5 (1982), 1063-1100.

140.              Classification of isolated hypersurface singularities by their moduli algebras (with John Mather), Invent. Math., Vol. 69 (1982), 243-251.

141.              S（n-1) invariant for isolated n-dimensional singularities and its application to moduli problem, Amer. J. Math., Vol. 104, No. 4 (1982), 829-841.

142.              Criterion for biholomorphic equivalence of isolated hypersurface singularities (with John Mather), Proc. Nat. Acad. Sci., U.S.A., Vol. 78 (1981), 5946-5947.

143.              Existence of L2-integrable holomorphic forms and lower estimates of T1_V, Duke Math. J., Vol. 48, No. 3 (1981), 537-547.

144.              Kohn-Rossi cohomology and its application to the complex Plateau problem, I, Ann. of Math., Vol. 113 (1981), 67-110.

145.              Deformations and equitopological deformations of strongly pseudoconvex manifolds, Nagoya Math. J., Vol. 82 (1981), 113-129.

146.              Index theory for the boundaries of complex analytic varieties, Proc. Nat. Acad. Sci. U.S.A., Vol. 77 (1980), 1248-1249.

147.              On maximally elliptic singularities, Trans. Amer. Math. Soc., Vol. 257 (1980), 269-329.

148.              Normal two-dimensional elliptic singularities, Trans. Amer. Math. Soc., Vol. 254 (1979), 117-134.

149.              On strongly elliptic singularities, Amer. J. Math., Vol. 101 (1979), 855-884.

150.              Gorenstein singularities with geometric genus equal to two, Amer. J. Math., Vol. 101 (1979), 813-854.

151.              Hypersurface weighted dual graphs of normal singularities of surfaces, Amer. J. Math., Vol. 101 (1979), 761-812.

152.              The signature of Milnor Fibres and duality theorem for strongly pseudoconvex manifolds, Invent. Math., Vol. 46 (1978), 81-97.

153.              Two theorems on higher dimensional singularities, Math. Ann., Vol. 231 (1977), 55 -59.