莫毅明科研成就

莫毅明科研成就科研综述莫毅明致力于多复变函数论、复微分几何与代数几何的研究,于1988年结合非线性偏微分方程领域的里奇流方法与代数几何领域里关于有理曲线的理论解决了广义弗兰克尔猜想

他引进了完备凯勒流形的代数几何化,并与来自中国科学院的数学家钟家庆教授合作证明了有限体积完备凯勒流形的紧致化定理

论文于1989年在《Annals of Mathematics》发表,为中国自20世纪70年代改革开放以来首篇有中国国内数学家为共同作者在该杂志发表的论文

莫毅明与合作者共同发展了一套运用极小有理曲线簇(VMRT)研究费诺流形的几何理论,于1998年通过此几何理论证明了不可约紧埃尔米特对称空间在凯勒形变下的刚性定理,并于1999年与2004年解答了代数几何领域的拉萨斯菲尔德问题

大约自2010年始,莫毅明开展其横跨代数几何、复微分几何与数论领域的研究工作

莫教授及其合作者致力发展一套关于充满直线之单直纹射影流形上的子流形的微分几何理论,并运用复微分几何方法解决有界对称域的商空间上一系列来自数论的几何难题

 学术论著截至2011年,莫毅明发表逾80篇研究论文,其中10篇刊登在《Annals of Mathematics》《Inventiones Mathematicae》等期刊内

 代表性著作(1986-2020)Metric rigidity theorems on locally symmetric Hermitian spaces, Proc. Natl. Acad. Sci. U.S.A. 83 (1986), 2288-2290.Uniqueness theorems of Hermitian metrics of seminegative curvature on locally symmetric spaces of negative Ricci curvature, Ann. Math. 125 (1987), 105-152.The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature, J. Differential Geom. 27 (1988), 179-214.Compactification of complete Kähler surfaces of finite volume satisfying certain curvature conditions, Ann. Math. 129 (1989), 383-425.(with J.-Q. Zhong) Compactifying complete Kähler-Einstein manifolds of finite topological type and bounded curvature, Ann. Math. 129 (1989), 427-470.(with H.-D. Cao) Holomorphic immersions between compact hyperbolic space forms, Invent. Math. 100 (1990), 49-61.Factorization of semisimple discrete representation of Kähler groups, Invent. Math. 110 (1992), 557-614.(with Y.-T. Siu and S.-K. Yeung) Geometric superrigidity, Invent. Math. 113 (1993), 57-83.(with J.-M. Hwang) Rigidity of irreducible Hermitian symmetric spaces of the compact type under Kähler deformation, Invent. Math. 131 (1998), 393-418.(with J.-M. Hwang) Holomorphic maps from rational homogeneous spaces of Picard number 1 onto projective manifolds, Invent. Math. 136 (1999), 209-231.Extremal bounded holomorphic functions and an embedding theorem for arithmetic varieties of rank ³ 2, Invent. Math. 158 (2004), 1-31.(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.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.(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.(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.(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.Extension of germs of holomorphic isometries up to normalizing constants with respect to the Bergman metric, J. Eur. Math. Soc. 14 (2012), 1617-1656.(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.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.(with J. Pila & J. Tsimerman) Ax-Schanuel for Shimura Varieties, Annals of Mathematics 189, no.3 (2019), 945-978.(with J. Hong) Schur rigidity of Schubert varieties in rational homogeneous manifolds of Picard number one, Selecta Mathematica 26, no.41, (2020).(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, accepted for publication in J. Differential Geom.  学术交流1980年,莫毅明应邀访问中国科学院并进行一个月关于复几何方面的专题演讲;此后多次与到访的中国国内优秀数学家合作研究

 1994年,莫毅明受邀在苏黎世举办的国际数学家大会(ICM)作45分钟学术报告

 2011年10月,莫毅明受中国科学院国家数学与交叉科学中心邀请,作题为《Holomorphic isometries and measure-preserving maps in Kähler geometry》的三场系列报告

 2018年12月,莫毅明受邀在北京国际数学研究中心举办的2018年“数学及其应用”教育部重点实验室年会上作题为《Uniformization of Certain Subvarieties of Finite-Volume Quotient Spaces of Bounded Symmetric Domains》的特邀报告

 2019年3月,莫毅明在中国科学院数学与系统科学研究院作题为《Curvature, Rescaling and Uniformization on Bounded Symmetric Domains》的学术报告

 科研成果奖励2008年1月,莫毅明独立完成的《关于对称与齐次空间的复几何》项目获得2007年度国家自然科学奖二等奖,为该年度全国数学学科仅有的两项获奖项目之一

  2022年12月,莫毅明作为主要完成人完成的《复微分几何及其应用》项目获得2022年度陈嘉庚科学奖数理科学奖

  

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