Continuous solutions to Monge–Ampère equations on Hermitian manifolds for measures dominated by capacity

Author:

Kołodziej Sławomir,Nguyen Ngoc Cuong

Abstract

AbstractWe prove the existence of a continuous quasi-plurisubharmonic solution to the Monge–Ampère equation on a compact Hermitian manifold for a very general measure on the right hand side. We admit measures dominated by capacity in a certain manner, in particular, moderate measures studied by Dinh–Nguyen–Sibony. As a consequence, we give a characterization of measures admitting Hölder continuous quasi-plurisubharmonic potential, inspired by the work of Dinh–Nguyen.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Analysis

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Continuous Solutions to Complex Hessian Equations on Hermitian Manifolds;The Journal of Geometric Analysis;2023-09-26

2. Quasi-plurisubharmonic envelopes 3: Solving Monge–Ampère equations on hermitian manifolds;Journal für die reine und angewandte Mathematik (Crelles Journal);2023-06-09

3. The Dirichlet problem for the Monge–Ampère equation on Hermitian manifolds with boundary;Calculus of Variations and Partial Differential Equations;2022-11-04

4. The complex Sobolev space and Hölder continuous solutions to Monge–Ampère equations;Bulletin of the London Mathematical Society;2022-04

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