Professor Ngaiming Mok
莫毅明教授

Research Interest:

Professor Mok's research interests encompass Several Complex Variables, Differential Geometry and Algebraic Geometry. His recent works in Complex Differential Geometry revolve around bounded symmetric domains, extremal bounded holomorphic functions, rigidity problems and holomorphic geodesic cycles on Hermitian locally symmetric spaces. In Algebraic Geometry his recent works are primarily related to Fano manifolds and more generally uniruled projective varieties. He is on the editorial boards of Inventiones mathematicae, Mathematische Annalen, Science in China, Series A (Mathematics), Chinese Annals of Mathematics, Series B and Journal de l'Institut de Mathématiques de Jussieu, Paris.

Lecture Notes:

• Ergodicity, bounded holomorphic functions and geometric structures in rigidity results on bounded symmetric domains, 2007. (pdf)
• Complex Geometry on Bounded Symmetric Domains, 2006.
  • I. Metric rigidity(pdf)
  • II. Geometric structures and III. Proper holomorphic maps and related problems(pdf)
• Characterization of Holomorphic Geodesic Cycles on Quotients of Bounded Symmetric Domains, 2005. (pdf)
• From Rational Curves to Complex Structures on Fano Manifolds, 2005. (pdf)

• Projective-algebraicity of minimal compactifications of complex-hyperbolic space forms of finite volume. (pdf)
• An isomorphism theorem for holomorphic mappings from arithmetic varieties of rank ³ 2 into quotients of bounded domains of finite intrinsic measure. (pdf)

• (with J. Hong) Characterization of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1, to appear in J. Alg. Geom. (pdf)
• Extension of germs of holomorphic isometries up to normalizing constants with respect to the Bergman metric, to appear in J. Eur. Math. Soc. (pdf)

• (with S.-C. Ng) Germs of measure-preserving holomorphic maps from bounded symmetric domains to their Cartesian products, J. Reine Angew. Math. (online publication), DOI 10.1515/CRELLE.2011.142, (27 pages). (pdf)
• On singularities of generically immersive holomorphic maps between complex hyperbolic space forms, in Complex and Differential Geometry, Proceedings of a conference at Leibniz Universität, Hannover (2009), Springer-Verlag, Berlin-Heidelberg 2011, pp.323-344. (pdf)
• Geometry of holomorphic isometries and related maps between bounded domains, in Geometry and Analysis, Vol. II, Advanced Lectures in Mathematics 18, Higher Educational Press, Beijing, 2011, pp.225-270. (pdf)
• (with J. Hong) Analytic continuation of holomorphic maps respecting varieties of minimal rational tangents and applications to rational homogeneous manifolds, J. Diff. Geom. 86 (2010), 539-567. (pdf)
• (with V. Koziarz) Nonexistence of holomorphic submersions between complex unit balls equivariant with respect to a lattice and their generalizations, Amer. J. Math. 132 (2010), 1347-1363. (pdf)
• On the Zariski closure of a germ of totally geodesic complex submanifold on a subvariety of a complex hyperbolic space form of finite volume, in Complex Analysis, Trends in Mathematics, ed. P. Ebenfelt, etc., Birkhäuser, Basel-Boston 2010, pp. 279-300. (pdf)
• (with S.-C. Ng and Z. Tu) Factorization of proper holomorphic maps on irreducible bounded symmetric domains of rank ³ 2, Science China Mathematics - Special Issue Dedicated to Professor Yang Lo on the Occasion of his 70th Birthday, 53 (2010), 813-826. (pdf)
• (with S.-C. Ng) Second fundamental forms of holomorphic isometries of the Poincaré disk into bounded symmetric domains and their boundary behavior along the unit circle, Science in China Series A: Mathematics - Dedicated to Professor ZHONG TongDe on the occasion of his 80th birthday, 52 (2009), 2628-2646. (pdf)
• On the asymptotic behavior of holomorphic isometries of the Poincaré disk into bounded symmetric domains, Special Volume in honor of Professor Wu Wenjun on the occasion of his 90th birthday, Acta Mathematica Scientia, 29B(4) (2009), 881-902. (pdf)
• (with X. Sun) Remarks on lines and minimal rational curves, Science in China Series A: Mathematics, 52 (2009), 617-630. (pdf)
• Geometric structures on uniruled projective manifolds defined by their varieties of minimal rational tangents, Proceedings of the Conference "Géometrie différentielle, Physique mathématique, Mathématique et Société", Astérisque, 322 (2008), Volume II, 151-205, published by Société Mathématique de France. (pdf)
• 有界全純函數與VMRT幾何理論在剛性問題上的應用，《多複變在中國的研究與發展》，第492-554頁，科技出版社，北京，2009。 (pdf)
• Recognizing certain rational homogeneous manifolds of Picard number 1 from their varieties of minimal rational tangents, AMS/IP Studies in Advanced Mathematics, 42 (2008), 41-61. (pdf)
• Nonexistence of proper holomorphic maps between certain classical bounded symmetric domains, Chinese Annals of Mathematics - Series B 29 (2008), 135-146. (pdf)
• Characterization of standard embeddings between complex Grassmannians by means of varieties of minimal rational tangents, Science in China Series A: Mathematics 51 (2008), 660-684. (pdf)
• Ergodicity, bounded holomorphic functions and geometric structures in rigidity results on bounded symmetric domains, in Proceedings of the International Congress of Chinese Mathematicians (Hangzhou 2007), Volume II, Higher Educational Press, Beijing, 2007, pp.464-505. (pdf)
• Rigidity problems on compact quotients of bounded symmetric domains, AMS/IP Studies in Advanced Mathematics 39 (2007), 201-249. (pdf)
• (with J.-M. Hwang) Prolongations of infinitesimal linear automorphisms of projective varieties and rigidity of rational homogeneous spaces of Picard number 1 under Kähler deformation, Invent. Math. 160 (2005), 591-645.(pdf)
• On holomorphic immersions into Kähler manifolds of constant holomorphic sectional curvature, Science in China Ser. A Mathematics 48 Supp. (2005), 123-145. (pdf)
• Extremal bounded holomorphic functions and an embedding theorem for arithmetic varieties of rank ³ 2, Invent. Math. 158 (2004), 1-31. (pdf)
• (with P. Eyssidieux) On the validity or failure of gap rigidity for certain pairs of bounded symmetric domains, Special Volume in memory of Professor Armand Borel, Asian J. Math. 8 (2004), 773-794. (pdf)
• (with J.-H. Hwang) Birationality of the tangent map for minimal rational curves, Special Volume dedicated to Professor Yum-Tong Siu on his sixtieth birthday, Asian J. Math. 8 (2004), 51-64. (pdf)
• (with J.-M. Hwang) Automorphism groups of the spaces of minimal rational curves on Fano manifolds of Picard Number 1, J. Alg. Geom. 13 (2004), 663-673.
• (with J.-M. Hwang) Deformation rigidity of the 20-dimensional F₄-homogeneous space associated to a short root. to appear in Algebraic Transformation Groups and Algebraic Varieties, ed. V.L. Popov, Encyclopaedia of Mathematical Sciences, Springer-Verlag, Berlin-Heidelberg-New York 2004.
• Negativity of curvature on spaces parametrizing Hodge decompositions of reduced first cohomology groups, Contemp. Math. 332 (2003), 219-234.
• (with J.-M. Hwang) Finite morphisms onto Fano manifolds of Picard number 1 which have curves with trivial normal bundle, J. Alg. Geom. 12 (2003), 627-652.
• Local holomorphic isometric embeddings arising from correspondences in the rank-1 case, in Contemporary Trends in Algebraic Geometry and Algebraic Topology, ed. S.-S. Chern, L. Fu and R. Hain, Nankai Tracts in Mathematics, Vol.5, World Scientific, New Jersey 2002, pp.155-166.
• (with J.-M. Hwang) Deformation rigidity of the rational homogeneous space associated to a long root, Ann. Scient. Ec. Norm. Sup. 35 (2002), 173-184.
• On Fano manifolds with nef tangent bundles admitting 1-dimensional varieties of minimal rational tangents, Trans. A.M.S. 354 (2002), 2639-2658.
• Characterization of certain holomorphic geodesic cycles on quotients of bounded symmetric domains in terms of tangent subspaces, Comp. Math. 132 (2002), 289-309
• (with J.-M. Hwang) Projective manifolds dominated by abelian varieties, Math. Zeit. 238 (2001), 89-150.
• (with J.-M. Hwang) Cartan-Fubini type extension of holomorphic maps for Fano manifolds of Picard number 1, J. Math. Pure Appl. 80 (2001), 563-575.
• Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups, Ann. Inst. Fourier 50 (2000), 633-675.
• (with J.-M. Hwang) Varieties of minimal rational tangents on uniruled manifolds, in Several Complex Variables , ed. M. Schneider and Y.-T. Siu, MSRI publications 37, Cambridge University Press, Cambridge 1999, pp.351-389.
• G-structures on irreducible Hermitian symmetric spaces of rank ³ 2 and deformation rigidity, Contemp. Math. 222, 1999, pp.81-107.
• (with J.-M. Hwang) Holomorphic maps from rational homogeneous spaces of Picard number 1 onto projective manifolds, Invent. Math. 136 (1999), 209-231.
• (with J.-M. Hwang) Characterization and deformation-rigidity of compact irreducible Hermitian symmetric spaces of rank ³ 2 among Fano manifolds, in Lectures in Algebra and Geometry , ed. Kang, M.-C., International Press, Cambridge, Mass., 1998, pp.15-46.
• (with J.-M. Hwang) Uniruled projective manifolds with irreducible reductive G-structures, J. Reine Angew. Math. 490 (1997), 55-64.
• (with J.-M. Hwang) Rigidity of irreducible Hermitian symmetric spaces of the compact type under Kähler deformation, Invent. Math. 131 (1998), 393-418.
• Steinness of universal coverings of certain compact Kähler manifolds, J. Reine Angew. Math. 498 (1997), 1-14.
• The generalized theorem of Castelnuovo-de Franchis for unitary representations, in Geometry from the Pacific Rim , ed. A.J. Berrick et al., de Gruyter, Berlin-New York 1997, pp.261-284.

Miscellaneous:

• Erratum to "Local holomorphic isometric embeddings arising from correspondences in the rank-1 case", 2005. (pdf)