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

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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.
作者 张教根 Jiaogen ZHANG(School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China)
机构地区 School of Mathematical Sciences
出处 《Acta Mathematica Scientia》 SCIE CSCD 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).
关键词 complex Monge-Ampere equation almost Hermitian manifold a priori estimate SUBSOLUTION J-plurisubharmonic
分类号 O186.1 [理学—基础数学]
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Acta Mathematica Scientia
2022年 第5期

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