A C0-estimate for the parabolic Monge-Ampere equation on complete non-compact Kahler manifolds

被引：6
|
作者：
Chau, Albert [1 ]
Tam, Luen-Fai [2 ,3 ]
机构：
[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
[3] Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China
来源：
COMPOSITIO MATHEMATICA | 2010年 / 146卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
non-compact Kahler-Einstein metrics; Kahler-Ricci flow; parabolic Monge-Ampere equation; RICCI FLOW; RIEMANNIAN-MANIFOLDS; EINSTEIN-METRICS; CURVATURE;
D O I：
10.1112/S0010437X09004369
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article we study the Kahler-Ricci flow, the corresponding parabolic Monge-Ampere equation and complete non-compact Kahler-Ricci flat manifolds. Our main result states that if (M, g) is sufficiently close to being Kahler-Ricci flat in a suitable sense, then the Kahler-Ricci flow has a long time smooth solution g(t) converging smoothly uniformly on compact sets to a complete Kahler-Ricci flat metric on M. The main step is to obtain a uniform C-0-estimate for the corresponding parabolic Monge-Ampere equation. Our results on this can be viewed as parabolic versions of the main results of Tian and Yau [Complete Kahler manifolds with zero Ricci. curvature. II, Invent. Math. 106 (1990), 27-60] on the elliptic Monge-Ampere equation.
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页码：259 / 270
页数：12
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