Vol. 14, No. 6, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 6, 1375–1616
Issue 5, 1131–1373
Issue 4, 891–1130
Issue 3, 567–890
Issue 2, 273–566
Issue 1, 1–272

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
$C^{1,1}$ regularity of degenerate complex Monge–Ampère equations and some applications

Jianchun Chu

Vol. 14 (2021), No. 6, 1671–1700
Abstract

We prove a C1,1 estimate for solutions of complex Monge–Ampère equations on compact almost Hermitian manifolds. Using this C1,1 estimate, we show the existence of C1,1 solutions to the degenerate Monge–Ampère equations, the corresponding Dirichlet problems and the singular Monge–Ampère equations. We also study the singularities of the pluricomplex Green’s function. In addition, the proof of the above C1,1 estimate is valid for a kind of complex Monge–Ampère-type equation. As a geometric application, we prove the C1,1 regularity of geodesics in the space of Sasakian metrics.

Keywords
degenerate complex Monge–Ampère equation, $C^{1,1}$ estimate
Mathematical Subject Classification 2010
Primary: 32W20
Secondary: 35J70, 53C15, 32Q60, 35J75, 53C25
Milestones
Received: 12 December 2018
Revised: 30 March 2019
Accepted: 16 March 2020
Published: 7 September 2021
Authors
Jianchun Chu
Institute of Mathematics
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
Beijing
China