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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)
22) Chen, Jingyi; Li, Jiayu, Mean curvature flow of surface in 4-manifolds - ADVANCES IN MATHEMATICS - 2001 - 163 (2)(2001)
23) Chen, Jingyi; Li, Jiayu, Quaternionic maps between hyperkahler manifolds - JOURNAL OF DIFFERENTIAL GEOMETRY - 2000 - 55 (2)(2000)
24) Ding, Weiyue; Jost, Juergen; Li, Jiayu; Peng, Xiaowei; Wang, Guofang, Self duality equations for Ginzburg-Landau and Seiberg-Witten type functionals with 6(th) order potentials - COMMUNICATIONS IN MATHEMATICAL PHYSICS - 2001 - 217 (2)(2001)
25) Li, Jiayu, Narasimhan, MS, A note on Hermitian-Einstein metrics on parabolic stable bundles - ACTA MATHEMATICA SINICA-ENGLISH SERIES - 2001 - 17 (1)(2001)
26) Li, Jiayu, Hermitian-Einstein metrics and Chern number inequalities on parabolic stable bundles over Kahler manifolds - COMMUNICATIONS IN ANALYSIS AND GEOMETRY - 2000 - 8 (3)(2000)
27) Li, Jiayu; Tian, Gang, The blow-up locus of heat flows for harmonic maps - ACTA MATHEMATICA SINICA-ENGLISH SERIES - 2000 - 16 (1)(2000)
28) Li, Jiayu; Wang, Silei, The heat flow of harmonic maps from noncompact manifolds - CHINESE ANNALS OF MATHEMATICS SERIES B - 2000 - 21 (1)(2000)
29) Li, Jiayu; Wang, Youde, Existence of Hermitian-Einstein metrics on stable Higgs bundles over open Kahler manifolds - INTERNATIONAL JOURNAL OF MATHEMATICS - 1999 - 10 (8)(1999)
30)  Ding, Weiyue; Jost, Juergen; Li, Jiayu; Wang, Guofang, Existence results for mean field equations - ANN DE L INST H POINCARE-ANALYSE NON LINEAR - 1999 - 16 (5)(1999)
31) Li, Jiayu; Wang, Youde, Parabolic stable Higgs bundles over complete noncompact Riemann surfaces - SCIENCE IN CHINA - 1999 - 42 (3)(1999)
32) Ding, Weiyue; Jost, Juergen; Li, Jiayu; Wang, Guofang, Multiplicity results for the two-vortex Chern-Simons Higgs model on the two-sphere - COMMENTARII MATHEMATICI HELVETICI - 1999 - 74 (1)(1999)
33) Li, Jiayu, Hermitian-Einstein metrics on parabolic stable bundles - ACTA MATHEMATICA SINICA-ENGLISH SERIES - 1999 - 15 (1)(1999)
34) Li, Jiayu; Wang, Silei, The heat flows and harmonic maps from complete manifolds into regular balls - BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY - 1998 - 58 (2)(1998)
35) Li, Jiayu; Tian, Gang, A blow-up formula for stationary harmonic maps - INTERNATIONAL MATHEMATICS RESEARCH NOTICES - 1998 - 14(1998)
36) Ding, Weiyue; Jost, Juergen; Li, Jiayu; Wang, Guofang, An analysis of the two-vortex case in the Chern-Simons Higgs model - CAL VAR PDE - 1998 - 7 (1)(1998)
37) Li, Jiayu, Hitchin's self-duality equations on complete Riemannian manifolds - MATHEMATISCHE ANNALEN - 1996 - 306 (3)(1996)
38) Ding, Weiyue; Jost, Jürgen; Li, Jiayu; Wang, Guofang, The differential equation $\Delta u=8\pi-8\pi he\sp u$ on a compact Riemann surface - Asian J. Math. - 1997 - 1(2) (1997)
39) Jost, Juergen; Li, Jiayu, Finite energy and totally geodesic maps from locally symmetric spaces of finite volume - CAL VAR PDE - 1996 - 4 (5)(1996)
40) Chen, Yunmei; Li, Jiayu; Lin, Fang-Hua, Partial regularity for weak heat flows into spheres - COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS - 1995 - 48 (4)(1995)
41) Li, Jiayu; Shao, Xin, On the upper estimates of fundamental solutions of parabolic equations on Riemannian manifolds - CHINESE ANNALS OF MATHEMATICS SERIES B - 1995 - 16 (1)(1995)
42) Li, Jiayu, Heat flows and harmonic maps with a free boundary - MATHEMATISCHE ZEITSCHRIFT - 1994 - 217 (3)(1994)
43) Li, Jiayu, Spectrum of the Laplacian on a complete Riemannian manifold with nonnegative Ricci curvature which possess a pole - JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN - 1994 - 46 (2)(1994)
44) Li, Jiayu, Boundedness of the Riesz potential on a complete manifold with nonnegative Ricci curvature - PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY - 1993 - 118 (4)(1993)
45) Li, Jiayu, On the Harnack inequality for harmonic functions on complete Riemannian manifolds - CHINESE ANNALS OF MATHEMATICS SERIES B - 1993 - 14 (1)(1993)
46) Li, Jiayu, The Heat flows and harmonic maps of complete noncompact Riemannian manifolds - MATHEMATISCHE ZEITSCHRIFT - 1993 - 212 (2)(1993)
47) Li, Jiayu, Gradient estimates and Harnack inequalities for Nonlinear parabolic and nonlinear elliptic equations on Riemannian manifolds - JOURNAL OF FUNCTIONAL ANALYSIS - 1991 - 100 (2)(1991)
48) Li, Jiayu, Gradient estimate for the heat kernel of a complete Riemannian manifold and its applications - JOURNAL OF FUNCTIONAL ANALYSIS - 1991 - 97 (2)(1991)
49) Chen, Jiecheng; Li, Jiayu, A note on eigenvalues - CHINESE SCIENCE BULLETIN - 1990 - 35 (7)(1990)
 
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