A SUBSOLUTION THEOREM FOR THE MONGE-AMPERE EQUATION OVER AN ALMOST HERMITIAN MANIFOLD  

作　　者：Jiaogen ZHANG 张教根(School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China

出　　处：《Acta Mathematica Scientia》2022年第5期2040-2062,共23页数学物理学报（B辑英文版）

基　　金：supported by the National Key R and D Program of China(2020YFA0713100).

摘　　要：Let Ω⊆M be a bounded domain with a smooth boundary ∂Ω,where(M,J,g)is a compact,almost Hermitian manifold.The main result of this paper is to consider the Dirichlet problem for a complex Monge-Ampère equation on Ω.Under the existence of a C^(2)-smooth strictly J-plurisubharmonic(J-psh for short)subsolution,we can solve this Dirichlet problem.Our method is based on the properties of subsolutions which have been widely used for fully nonlinear elliptic equations over Hermitian manifolds.

关 键 词：complex Monge-Ampere equation almost Hermitian manifold a priori estimate SUBSOLUTION J-plurisubharmonic 

分 类 号：O186.1[理学—数学]