Continuous solutions to Monge-Amp\`ere equations on Hermitian manifolds for measures dominated by capacity
Complex Variables
2020-03-12 v1 Differential Geometry
Dynamical Systems
Abstract
We prove the existence of a continuous quasi-plurisubharmonic solution to the Monge-Amp\`ere equation on a compact Hermitian manifold for a very general measre 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 H\"older continuous quasi-plurisubharmonic potential, inspired by the work of Dinh-Nguyen.
Keywords
Cite
@article{arxiv.2003.05061,
title = {Continuous solutions to Monge-Amp\`ere equations on Hermitian manifolds for measures dominated by capacity},
author = {Slawomir Kolodziej and Ngoc Cuong Nguyen},
journal= {arXiv preprint arXiv:2003.05061},
year = {2020}
}
Comments
18 pages