C-1,C-1 REGULARITY OF DEGENERATE COMPLEX MONGE-AMPERE EQUATIONS AND SOME APPLICATIONS

doi:10.2140/apde.2021.14.1671

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	C-1,C-1 REGULARITY OF DEGENERATE COMPLEX MONGE-AMPERE EQUATIONS AND SOME APPLICATIONS
	Chu, Jianchun
	2021
发表期刊	ANALYSIS & PDE
ISSN	1948-206X
卷号	14 期号:6 页码:1671-1700
摘要	We prove a C-1,C-1 estimate for solutions of complex Monge-Ampere equations on compact almost Hermitian manifolds. Using this C-1,C-1 estimate, we show the existence of C-1,C-1 solutions to the degenerate Monge-Ampere equations, the corresponding Dirichlet problems and the singular Monge-Ampere equations. We also study the singularities of the pluricomplex Green's function. In addition, the proof of the above C-1,C-1 estimate is valid for a kind of complex Monge-Ampere-type equation. As a geometric application, we prove the C-1,C-1 regularity of geodesics in the space of Sasakian metrics.
关键词	degenerate complex Monge-Ampere equation C-1,C-1 estimate
DOI	10.2140/apde.2021.14.1671
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000693610100001
出版者	MATHEMATICAL SCIENCE PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59231
专题	中国科学院数学与系统科学研究院
通讯作者	Chu, Jianchun
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Chu, Jianchun. C-1,C-1 REGULARITY OF DEGENERATE COMPLEX MONGE-AMPERE EQUATIONS AND SOME APPLICATIONS[J]. ANALYSIS & PDE,2021,14(6):1671-1700.
APA	Chu, Jianchun.(2021).C-1,C-1 REGULARITY OF DEGENERATE COMPLEX MONGE-AMPERE EQUATIONS AND SOME APPLICATIONS.ANALYSIS & PDE,14(6),1671-1700.
MLA	Chu, Jianchun."C-1,C-1 REGULARITY OF DEGENERATE COMPLEX MONGE-AMPERE EQUATIONS AND SOME APPLICATIONS".ANALYSIS & PDE 14.6(2021):1671-1700.