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

doi:10.1007/s10473-022-0518-9

Abstract

Abstract: 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 C²-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.

Key words: complex Monge-Ampère equation, almost Hermitian manifold, a priori estimate, subsolution, J-plurisubharmonic

CLC Number:

32W20

Jiaogen ZHANG. A SUBSOLUTION THEOREM FOR THE MONGE-AMPÈRE EQUATION OVER AN ALMOST HERMITIAN MANIFOLD[J].Acta mathematica scientia,Series B, 2022, 42(5): 2040-2062.

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