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李嘉禹
单位:数学科学学院
地址:中国科学技术大学数学系
邮编:230026
电话:+86-551-3603065
个人主页: http://dsxt.ustc.edu.cn/zj_js.asp?zzid=1798
实验室介绍:
个人简历
Personal resume
李嘉禹教授获得过百人计划、杰出青年基金等的资助,在几何分析领域取得了重要研究成果。在非线性方程解的紧性与奇点研究这一重要且困难的课题中,研究了一般情况下稳定调和映照的紧性,得到了有关弱极限和能量集中集的奇点公式,提出了弱极限稳定的充要条件并举例加以说明,把该困难问题的研究向前推进了一步。构造一个新的发展方程来研究极小曲面的存在性问题。证明了非紧情况下Narasimhan-Seshadri、Donaldson、Uhlenbeck-丘成桐定理,得到了稳定抛物丛上的陈数不等式,成为研究模空间的基础。在Kazdan-Warner 问题、高余维平均曲率流等方面的研究也取得了重要突破。
曾在联合国教科文组织-国际理论物理中心ICTP任研究员(2004年至2009年),负责几何与分析国际合作方面的工作,为发展中国等第三世界国家的数学科学做出贡献。曾获中国数学会陈省身数学奖、香港求是科技基金会杰出青年学者奖等。
研究方向
Research direction
1、几何分析
2、复几何
3、整体微分几何
招生信息
Enrollment information
部分学生在读期间可能被派往国际其他研究中心联合培养。
论文专著
The monograph
1) Han, Xiaoli; Li, Jiayu, Symplectic critical surfaces in Kahler surfaces - JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY - 2010 - 12 (2)(2010)
2) Li, Jiayu; Zhu, Xiangrong, Non existence of quasi-harmonic spheres - CAL VAR PDE - 2010 - 37 (3-4)(2010)
3) Li, Jiayu, Variational approach to various nonlinear problems in geometry and physics - FRONTIERS OF MATHEMATICS IN CHINA - 2008 - 3 (2)(2008)
4) Han, Xiaoli; Li, Jiayu, Translating solitons to symplectic and Lagrangian mean curvature flows - INTERNATIONAL JOURNAL OF MATHEMATICS - 2009 - 20 (4)(2009)
5) Li, Jiayu; Wang, Meng, Liouville theorems for self-similar solutions of heat flows - JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY - 2009 - 11 (1)(2009)
6) Hsu, Deliang; Li, Jiayu, On the regularity for stationary harmonic maps - ACTA MATHEMATICA SINICA-ENGLISH SERIES - 2008 - 24 (2)(2008)
7) Lan, Xiaohong; Li, Jiayu, Asymptotic behavior of the Chern-Simons Higgs 6-th theory - COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS - 2007 - 32 (10-12)(2007)
8) Chen, Qun; Jost, Juergen; Li, Jiayu; Wang, Guofang, Dirac-harmonic maps - MATHEMATISCHE ZEITSCHRIFT - 2006 - 254 (2)(2006)
9) Ding, Weiyue; Li, Jiayu; Liu, Qingyue, Evolution of minimal torus in Riemannian manifolds - INVENTIONES MATHEMATICAE - 2006 - 165 (2)(2006)
10) Han, Xiaoli; Li, Jiayu, The mean curvature flow approach to the symplectic isotopy problem - INTERNATIONAL MATHEMATICS RESEARCH NOTICES - 2005 - 26(2005)
11) Li, Jiayu; Li, Yuxiang, Solutions for Toda systems on Riemann surfaces - ANN DE SCU NORMALE SUPERIORE DI PISA - 2005 - 4 (4)(2005)
12) Chen, Jingyi; Li, Jiayu, Quaternionic maps and minimal surfaces - ANN DE SCU NORMALE SUPERIORE DI PISA - 2005 - 4 (3)(2005)
13) Chen, Qun; Jost, Juergen; Li, Jiayu; Wang, Guofang, Regularity theorems and energy identities for Dirac-harmonic maps - MATHEMATISCHE ZEITSCHRIFT - 2005 - 251 (1)(2005)
14) Li, Jiayu; Zhang, Xi, Quaternionic maps between quaternionic Kahler manifolds - MATHEMATISCHE ZEITSCHRIFT - 2005 - 250 (3)(2005)
15) Li, Jiayu; Sheng, Weimin, Deforming metrics with negative curvature by a fully nonlinear flow - CAL VAR PDE - 2005 - 23 (1)(2005)
16) Chen, Jingyi; Li, Jiayu, Singularity of mean curvature flow of Lagrangian submanifolds - INVENTIONES MATHEMATICAE - 2004 - 156 (1)(2004)
17) Guo, Zongming; Li, Jiayu, Partial regularity for weak solutions of semilinear elliptic equations with supercritical exponents - PACIFIC JOURNAL OF MATHEMATICS - 2004 - 214 (1)(2004)
18) Ding, Weiyue; Fan, Huijun; Li, Jiayu, Harmonic Hopf constructions between spheres II - CAL VAR PDE - 2003 - 16 (3)(2003)
19) Ding, Weiyue; Li, Jiayu; Li, Wei, Nonstationary weak limit of a stationary harmonic map sequence - COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS - 2003 - 56 (2)(2003)
20) Guo, Zongming; Li, Jiayu, The blow up locus of semilinear elliptic equations with supercritical exponents - CAL VAR PDE - 2002 - 15 (2)(2002)
21) Chen, Jingyi; Li, Jiayu; Tian, Gang, Two-dimensional graphs moving by mean curvature flow - ACTA MATHEMATICA SINICA-ENGLISH SERIES - 2002 - 18 (2)(2002)