Deforming metrics with negative curvature by a fully nonlinear flow

被引：29
作者：
Li, JY [1 ]
Sheng, WM
机构：
[1] Chinese Acad Sci, Inst Math, Beijing 100080, Peoples R China
[2] Zhejiang Univ, Dept Math, Hangzhou 310028, Peoples R China
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2005年 / 23卷 / 01期
关键词：
D O I：
10.1007/s00526-004-0287-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
By studying a fully nonlinear flow deforming conformal metrics on compact and connected manifold, we prove that for lambda < 1, any metric g with its modified Schouten tensor A(g)(lambda) is an element of Gamma(-)(k) always can be deformed in a natural way to a conformal metric with constant sigma(k)-scalar curvature at exponential rate.
引用
收藏
页码：33 / 50
页数：18
相关论文
共 24 条
[1]  
ANDREW G, 1997, INT MATH RES NOTICES, P1001
[2]  
BRENDLE S, IN PRESS CALC VAR
[3]  
BROOKS R, 1989, J DIFFER GEOM, V29, P85
[4]   An a priori estimate for a fully nonlinear equation on four-manifolds [J].
Chang, SYA ;
Gursky, MJ ;
Yang, P .
JOURNAL D ANALYSE MATHEMATIQUE, 2002, 87 (1) :151-186
[5]   An equation of Monge-Ampere type in conformal geometry, and four-manifolds of positive Ricci curvature [J].
Chang, SYA ;
Gursky, MJ ;
Yang, PC .
ANNALS OF MATHEMATICS, 2002, 155 (03) :709-787
[6]   A variational theory of the Hessian equation [J].
Chou, KS ;
Wang, XJ .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2001, 54 (09) :1029-1064
[7]   A logarithmic Gauss curvature flow and the Minkowski problem [J].
Chou, KS ;
Wang, XJ .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2000, 17 (06) :733-751
[8]   THE YAMABE FLOW ON LOCALLY CONFORMALLY FLAT MANIFOLDS WITH POSITIVE RICCI CURVATURE [J].
CHOW, B .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1992, 45 (08) :1003-1014
[9]  
Guan PF, 2003, J REINE ANGEW MATH, V557, P219
[10]  
Guan PF, 2003, INT MATH RES NOTICES, V2003, P1413
123