On the modulus of continuity of solutions to complex Monge-Amp\`ere equations
Differential Geometry
2021-12-07 v1 Analysis of PDEs
Complex Variables
Abstract
In this paper, we prove a uniform and sharp estimate for the modulus of continuity of solutions to complex Monge-Amp\`ere equations, using the PDE-based approach developed by the first three authors in their approach to supremum estimates for fully non-linear equations in K\"ahler geometry. As an application, we derive a uniform diameter bound for K\"ahler metrics satisfying certain Monge-Amp\`ere equations.
Keywords
Cite
@article{arxiv.2112.02354,
title = {On the modulus of continuity of solutions to complex Monge-Amp\`ere equations},
author = {Bin Guo and Duong H. Phong and Freid Tong and Chuwen Wang},
journal= {arXiv preprint arXiv:2112.02354},
year = {2021}
}
Comments
14 pages