Uniform entropy and energy bounds for fully non-linear equations
Differential Geometry
2022-07-20 v1 Analysis of PDEs
Complex Variables
Abstract
Energy bounds which are uniform in the background metric are obtained from upper bounds for entropy-like quantities. The argument is based on auxiliary Monge-Amp\`ere equations involving sublevel sets, and bypasses the Alexandrov-Bakelman-Pucci maximum principle. In particular, it implies uniform bounds for systems coupling a fully non-linear equation to its linearization, generalizing the cscK equation.
Cite
@article{arxiv.2207.08983,
title = {Uniform entropy and energy bounds for fully non-linear equations},
author = {Bin Guo and Duong H. Phong},
journal= {arXiv preprint arXiv:2207.08983},
year = {2022}
}