Professor
Ngaiming Mok Edmund and Peggy Tse Professor in Mathematics
莫毅明教授
Research Interests:
Areas of Specialization: Several
Complex Variables, Complex Differential Geometry, Algebraic Geometry,
Functional Transcendence Theory
Memberships of Academies and Learned Societies:
Academician of the Chinese Academy of Sciences Fellow of the Hong Kong
Academy of Sciences Fellow of the American Mathematical Society
Current Editorial Boards: Mathematische
Annalen Science China Mathematics Chinese Annals of
Mathematics
Education
and Academic Positions
Prizes,
Awards and Honors
List of Representative
Publications
Memberships
of Editorial Boards
List of
Representative Lectures
Scientific Contributions: An Overview
Biography (at Hong Kong
Academy of Sciences)
Poetry
Publications:
Publications since 1997
- (with S.-T. Chan)
Asymptotic total geodesy of local holomorphic curves exiting a bounded
symmetric domain and applications to a uniformization problem for
algebraic subsets, J. Differential Geom., 120, (2022), 1-49. (pdf)
- (with J. Hong) Schur
rigidity of Schubert varieties in rational homogeneous manifolds of Picard
number one, Selecta Mathematica 26, no.41, (2020). (pdf)
- Rigidity of certain
admissible pairs of rational homogeneous spaces of Picard number 1 which
are not of the subdiagram type, Sci. China Math. 62, (2019),
2335–2354. (pdf)
- Zariski closures of
images of algebraic subsets under the uniformization map on finite-volume
quotients of the complex unit ball, Compositio Math. 155,
(2019), 2129-2149. (pdf)
- (with J. Pila &
J. Tsimerman) Ax-Schanuel for Shimura Varieties, Annals of Mathematics
189, no.3 (2019), 945-978. (pdf)
- (with Y. Zhang)
Rigidity of pairs of rational homogeneous spaces of Picard number 1 and
analytic continuation of geometric substructures on uniruled projective
manifolds, J. Differential Geom 112, no.2 (2019), 263-345. (pdf)
- Some recent results
on holomorphic isometries of the complex unit ball into bounded symmetric
domains, in Geometric Complex Analysis, Proceedings Volume of the
KSCV12 Symposium, pp.269-290, Springer Proceedings in Mathematics & Statistics,
Springer Verlag, Singapore, 2018. (pdf)
- Full cones swept out
by minimal rational curves on irreducible Hermitian symmetric spaces as
examples of varieties underlying geometric substructures, in Local and
Global Methods in Algebraic Geometry, pp.261-285, Contemp. Math.,
Amer. Math. Soc., Providence, RI, 2018. (pdf)
- (with S.-C. Ng) On
compact splitting complex submanifolds of quotients of bounded symmetric
domains, Sci. China Math. 60, no.6 (2017), 1057-1076. (pdf)
- (with S.-T. Chan)
Holomorphic isometries of $\mathbb B^m$ into bounded symmetric domains
arising from linear sections of minimal embeddings of their compact duals,
Mathematische Zeitschrift. (pdf)
- Geometric structures
and substructures on uniruled projective manifolds, in Foliation Theory
in Algebraic Geometry (Simons Symposia), ed. P. Cascini, J.
McKernan and J.V. Pereira, Springer-Verlag, Heidelberg-New York-London
2016, pp.103-148. (pdf)
- Holomorphic
isometries of the complex unit ball into irreducible bounded symmetric
domains, Proc. A.M.S. 144 (2016), 4515-4525. (pdf)
- Local holomorphic
curves on a bounded symmetric domain in its Harish-Chandra realization
exiting at regular points of the boundary, J. Pure Appl. Math. Quart.
10 (2014), 259-288. (pdf)
- Uniqueness modulo
reduction of Bergman meromorphic compactifications of canonically
embeddable Bergman manifolds, in Frontiers in Differential Geometry,
Partial Differential Equations and Mathematical Physics, volume in
memory of Gu Chaohao, World-Scientific, New Jersey-Singapore 2014, pp.
271-290. (pdf)
- (with J. Hong)
Characterization of smooth Schubert varieties in rational homogeneous
manifolds of Picard number 1, J. Alg. Geom. 22 (2013),
333-362. (pdf)
- Extension of germs
of holomorphic isometries up to normalizing constants with respect to the
Bergman metric, J. Eur. Math. Soc. 14 (2012), 1617-1656. (pdf)
- Projective-algebraicity
of minimal compactifications of complex-hyperbolic space forms of finite
volume, Perspectives in Analysis, Geometry, Topology, Progr. Math.,
296, Birkhäuser/Springer, New York, 2012, pp.331-354. (pdf)
- (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.(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.
Differential 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.
Preprints:
- (with K.-K. Wong) Extension
of inverses of Ã-equivariant holomorphic embeddings of bounded symmetric domains
of rank ≥ 2 and applications to rigidity problems. (pdf)
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)
Miscellaneous:
- Erratum to
"Local holomorphic isometric embeddings arising from correspondences
in the rank-1 case", 2005. (pdf)