THE COMPLEX MONGE-AMPERE EQUATION ON SOME COMPACT HERMITIAN MANIFOLDS

被引：3
作者：
Chu, Jianchun [1 ]
机构：
[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
来源：
PACIFIC JOURNAL OF MATHEMATICS | 2015年 / 276卷 / 02期
关键词：
complex Monge-Ampere equation; compact Hermitian manifold; DIRICHLET PROBLEM;
D O I：
10.2140/pjm.2015.276.369
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the complex Monge-Ampere equation on compact manifolds when the background metric is a Hermitian metric (in complex dimension 2) or a Hermitian metric satisfying an additional condition (in higher dimensions). We prove that the Laplacian estimate holds when F is in W-1,W-q0 for any q(0) > 2n. As an application, we show that, up to scaling, there exists a unique classical solution in W-3,W-q0 for the complex Monge-Ampere equation when F is in W-1,W-q0.
引用
收藏
页码：369 / 386
页数：18
相关论文
共 29 条
[1]  
Aubin T., 1998, SOME NONLINEAR PROBL, DOI 10.1007/978-3-662-13006-3
[2]   DIRICHLET PROBLEM FOR A COMPLEX MONGE-AMPERE EQUATION [J].
BEDFORD, E ;
TAYLOR, BA .
INVENTIONES MATHEMATICAE, 1976, 37 (01) :1-44
[3]   A NEW CAPACITY FOR PLURISUBHARMONIC-FUNCTIONS [J].
BEDFORD, E ;
TAYLOR, BA .
ACTA MATHEMATICA, 1982, 149 (1-2) :1-40
[4]   On uniform estimate in Calabi-Yau theorem [J].
Blocki, Z .
SCIENCE IN CHINA SERIES A-MATHEMATICS, 2005, 48 :244-247
[5]   THE DIRICHLET PROBLEM FOR NONLINEAR 2ND-ORDER ELLIPTIC-EQUATIONS .2. COMPLEX MONGE-AMPERE, AND UNIFORMLY ELLIPTIC, EQUATIONS [J].
CAFFARELLI, L ;
KOHN, JJ ;
NIRENBERG, L ;
SPRUCK, J .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1985, 38 (02) :209-252
[6]  
Calabi E., 1954, PRINCETON MATH SERIE, V12, P78
[7]   The complex Monge-AmpSre equation on compact Kahler manifolds [J].
Chen, Xiuxiong ;
He, Weiyong .
MATHEMATISCHE ANNALEN, 2012, 354 (04) :1583-1600
[8]  
CHERRIER P, 1987, B SCI MATH, V111, P343
[9]   DEGENERATE COMPLEX MONGE-AMPERE EQUATIONS OVER COMPACT KAHLER MANIFOLDS [J].
Demailly, Jean-Pierre ;
Pali, Nefton .
INTERNATIONAL JOURNAL OF MATHEMATICS, 2010, 21 (03) :357-405
[10]   Uniqueness in ε(X, ω) [J].
Dinew, Slawomir .
JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 256 (07) :2113-2122
123