Complex Monge-Ampere equations and totally real submanifolds

被引：83
作者：
Guan, Bo [1 ]
Li, Qun [1 ]
机构：
[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA
来源：
ADVANCES IN MATHEMATICS | 2010年 / 225卷 / 03期
关键词：
Complex Monge-Ampere equations; Dirichlet problem; Hermitian manifolds; Totally real submanifolds; CONSTANT GAUSS CURVATURE; COMPACT HERMITIAN-MANIFOLDS; KAHLER-EINSTEIN METRICS; BOUNDARY-VALUE-PROBLEMS; CALABI-YAU EQUATION; DIRICHLET PROBLEM; PLURISUBHARMONIC-FUNCTIONS; RIEMANNIAN-MANIFOLDS; INTRINSIC NORMS; RICCI CURVATURE;
D O I：
10.1016/j.aim.2010.03.019
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the Dirichlet problem for complex Monge-Ampere equations in Hermitian manifolds with general (non-pseudoconvex) boundary. Our main result (Theorem 1.1) extends the classical theorem of Caffarelli, Kohn, Nirenberg and Spruck in C-n. We also consider the equation on compact manifolds without boundary, attempting to generalize Yau's theorems in the Kahler case. As applications of the main result we study some connections between the homogeneous complex Monge-Ampere (HCMA) equation and totally real submanifolds, and a special Dirichlet problem for the HCMA equation related to Donaldson's conjecture on geodesics in the space of Kahler metrics. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：1185 / 1223
页数：39
相关论文
共 71 条
12345678