The 2-dimensional Calabi flow

被引：8

作者：

Chang, SC ^{[1
]}

机构：

[1] Natl Tsing Hua Univ, Dept Math, Hsinchu 30043, Taiwan

来源：

NAGOYA MATHEMATICAL JOURNAL | 2006年 / 181卷

关键词：

D O I：

10.1017/S0027763000025678

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, based on a Harnack-type estimate and a local Sobolev constant bounded for the Calabi flow on closed surfaces, we extend author's previous results and show the long-time existence and convergence of solutions of 2-dimensional Calabi flow on closed surfaces. Then we establish the uniformization theorem for closed surfaces.

引用

收藏

页码：63 / 73

页数：11

相关论文

共 13 条

[1]

Calabi E, 1982, SEMINARS DIFFERENTIA, P259

[2]

Calabi E., 1985, DIFFERENTIAL GEOMETR, P95

[3] CRITICAL RIEMANNIAN 4-MANIFOLDS [J].

CHANG, SC .

MATHEMATISCHE ZEITSCHRIFT, 1993, 214 (04) :601-625

[4] On the existence of extremal metrics for L2-norm of scalar curvature on closed 3-manifolds [J].

Chang, SC ;

Wu, JT .

JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1999, 39 (03) :435-454

[5] Global existence and convergence of solutions of Calabi flow on surfaces of genus h≥2 [J].

Chang, SC .

JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 2000, 40 (02) :363-377

[6]

Chang SC, 2005, CONTEMP MATH, V367, P17

[7] Global existence and convergence of solutions of the Calabi flow on Einstein 4-manifolds [J].

Chang, SC .

NAGOYA MATHEMATICAL JOURNAL, 2001, 163 :193-214

[8] Calabi flow in Riemann surfaces revisited: A new point of view [J].

Chen, XX .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2001, 2001 (06) :275-297

[9] SEMIGLOBAL EXISTENCE AND CONVERGENCE OF SOLUTIONS OF THE ROBINSON-TRAUTMAN (2-DIMENSIONAL CALABI) EQUATION [J].

CHRUSCIEL, PT .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1991, 137 (02) :289-313

[10]

CROKE CB, 1980, ANN SCI ECOLE NORM S, V13, P419