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*

**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 F
_{4}-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)