Solutions to degenerate complex Hessian equations

被引：44

作者：

Chinh, Lu Hoang ^{[1
,2
]}

机构：

[1] Univ Toulouse 3, Inst Math Toulouse, 118 Route Narbonne, F-31062 Toulouse, France

[2] Univ Pedag, Dept Math, Ho Chi Minh City, Vietnam

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2013年 / 100卷 / 06期

关键词：

Kahler manifold; (omega; m)-subharmonic; Hessian operator; Weak solution; MONGE-AMPERE EQUATION; DIRICHLET PROBLEM; PLURISUBHARMONIC-FUNCTIONS; WEAK SOLUTIONS; INEQUALITY;

D O I：

10.1016/j.matpur.2013.03.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (X, omega) be an n-dimensional compact Kahler manifold and fix an integer in such that 1 <= m <= n. We study degenerate complex Hessian equations of the form (omega + dd(c)phi)(m) boolean AND omega(n-m) = F (x, phi)omega(n). Under some natural conditions on F, this equation has a unique continuous solution. When X is homogeneous and omega is invariant under the Lie group action, we further show that the solution is Holder continuous. (C) 2013 Elsevier Masson SAS. All rights reserved.

引用

页码：785 / 805

页数：21

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