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
List of Representative
Publications
Memberships
of Editorial Boards
List of
Representative Lectures
Scientific Contributions: An Overview
Biography (at Hong Kong
Academy of Sciences)
Publications:
Publications since 1997
- (with Ng,
S.-C.) Multiplicities of the Betti map
associated to a section of an elliptic surface from a differential-geometric erspective, J. Geom. Analysis,
DOI: 10.1007/s12220-023-01256-3 (pdf)
- Holomorphic
retractions of bounded symmetric domains onto totally geodesic complex submanifolds, Chinese Ann. Math., Series B 43 (2023), 1125-1142. (pdf)
- (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 Kim, S.-Y. and
Seo, A.) Proper holomorphic maps
between bounded symmetric domains with small rank differences. Preprint.
(pdf)
- (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)