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

Access to Document

10.1007/s12220-020-00540-w

Cite this

@article{7b3daa583f354c3e83a4893b288ca79d,

title = "The Dirichlet Problem on Almost Hermitian Manifolds",

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",

note = "Publisher Copyright: {\textcopyright} 2020, Mathematica Josephina, Inc.",

year = "2021",

month = jun,

doi = "10.1007/s12220-020-00540-w",

language = "English",

volume = "31",

pages = "6452--6480",

journal = "Journal of Geometric Analysis",

issn = "1050-6926",

publisher = "Springer New York",

number = "6",

}

TY - JOUR

T1 - The Dirichlet Problem on Almost Hermitian Manifolds

AU - Li, Chang

AU - Zheng, Tao

PY - 2021/6

Y1 - 2021/6

N2 - 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.

AB - 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.

KW - A priori estimate

KW - Almost Hermitian manifold

KW - Degenerate Monge–Ampère equation

KW - Dirichlet problem

KW - Monge–Ampère type equation

UR - http://www.scopus.com/inward/record.url?scp=85093968252&partnerID=8YFLogxK

U2 - 10.1007/s12220-020-00540-w

DO - 10.1007/s12220-020-00540-w

M3 - Article

AN - SCOPUS:85093968252

SN - 1050-6926

VL - 31

SP - 6452

EP - 6480

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 6

ER -

The Dirichlet Problem on Almost Hermitian Manifolds

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this