Professor Ngaiming Mok

Research Interests:

Professor Mok’s recent works in Complex Differential Geometry revolve around bounded symmetric domains, holomorphic isometries and measure-preserving maps, 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 Mathematische Annalen, Science China Mathematics and Chinese Annals of Mathematics.

Link to Croucher



Publications since 1997


List of Representative Publications (1986-2012):

  1. Metric rigidity theorems on locally symmetric Hermitian spaces, Proc. Natl. Acad. Sci. U.S.A. 83 (1986), 2288-2290.
  2. Uniqueness theorems of Hermitian metrics of seminegative curvature on locally symmetric spaces of negative Ricci curvature, Ann. Math. 125 (1987), 105-152.
  3. The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature, J. Differential Geom. 27 (1988), 179-214.
  4. Compactification of complete Kähler surfaces of finite volume satisfying certain curvature conditions, Ann. Math. 129 (1989), 383-425.
  5. (with J.-Q. Zhong) Compactifying complete Kähler-Einstein manifolds of finite topological type and bounded curvature, Ann. Math. 129 (1989), 427-470.
  6. (with H.-D. Cao) Holomorphic immersions between compact hyperbolic space forms, Invent. Math. 100 (1990), 49-61.
  7. Factorization of semisimple discrete representation of Kähler groups, Invent. Math. 110 (1992), 557-614.
  8. (with Y.-T. Siu and S.-K. Yeung) Geometric superrigidity, Invent. Math. 113 (1993), 57-83.
  9. (with J.-M. Hwang) Rigidity of irreducible Hermitian symmetric spaces of the compact type under Kähler deformation, Invent. Math. 131 (1998), 393-418.
  10. (with J.-M. Hwang) Holomorphic maps from rational homogeneous spaces of Picard number 1 onto projective manifolds, Invent. Math. 136 (1999), 209-231.
  11. Extremal bounded holomorphic functions and an embedding theorem for arithmetic varieties of rank ³ 2, Invent. Math. 158 (2004), 1-31.
  12. (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.
  13. 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.
  14. (with J. Hong) Analytic continuation of holomorphic maps respecting varieties of minimal rational tangents and applications to rational homogeneous manifolds, J. Differential Geom. 86 (2010), 539-567.
  15. (with S.-C. Ng) Germs of measure-preserving holomorphic maps from bounded symmetric domains to their Cartesian products, J. Reine Angew. Math.669, (2012), 47-73.
  16. Extension of germs of holomorphic isometries up to normalizing constants with respect to the Bergman metric, J. Eur. Math. Soc. 14 (2012), 1617-1656.
Lecture Notes: