The Dirichlet Problem on Almost Hermitian Manifolds

Chang Li; Tao Zheng

doi:10.1007/s12220-020-00540-w

The Dirichlet Problem on Almost Hermitian Manifolds

Chang Li, Tao Zheng^*

^*Corresponding author for this work

School of Mathematics and Statistics

CAS - Academy of Mathematics and System Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We prove second-order a priori estimate on the boundary for the Dirichlet problem of a class of fully nonlinear equations on compact almost Hermitian manifolds with smooth boundary. As applications, we solve the Dirichlet problem of the Monge–Ampère type equation and of the degenerate Monge–Ampère equation.

Original language	English
Pages (from-to)	6452-6480
Number of pages	29
Journal	Journal of Geometric Analysis
Volume	31
Issue number	6
DOIs	https://doi.org/10.1007/s12220-020-00540-w
Publication status	Published - Jun 2021

Keywords

A priori estimate
Almost Hermitian manifold
Degenerate Monge–Ampère equation
Dirichlet problem
Monge–Ampère type equation

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10.1007/s12220-020-00540-w

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Li, C., & Zheng, T. (2021). The Dirichlet Problem on Almost Hermitian Manifolds. Journal of Geometric Analysis, 31(6), 6452-6480. https://doi.org/10.1007/s12220-020-00540-w

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abstract = "We prove second-order a priori estimate on the boundary for the Dirichlet problem of a class of fully nonlinear equations on compact almost Hermitian manifolds with smooth boundary. As applications, we solve the Dirichlet problem of the Monge–Amp{\`e}re type equation and of the degenerate Monge–Amp{\`e}re equation.",

keywords = "A priori estimate, Almost Hermitian manifold, Degenerate Monge–Amp{\`e}re equation, Dirichlet problem, Monge–Amp{\`e}re type equation",

author = "Chang Li and Tao Zheng",

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KW - Degenerate Monge–Ampère equation

KW - Dirichlet problem

KW - Monge–Ampère type equation

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The Dirichlet Problem on Almost Hermitian Manifolds

Abstract

Keywords

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