Sup-slopes and sub-solutions for fully nonlinear elliptic equations
Analysis of PDEs
2024-05-07 v1 Differential Geometry
Abstract
We establish a necessary and sufficient condition for solving a general class of fully nonlinear elliptic equations on closed Riemannian or hermitian manifolds, including both hessian and hessian quotient equations. It settles an open problem of Li and Urbas. Such a condition is based on an analytic slope invariant analogous to the slope stability and the Nakai-Moishezon criterion in complex geometry. As an application, we solve the non-constant -equation on both hermitian manifolds and singular K\"ahler spaces.
Cite
@article{arxiv.2405.03074,
title = {Sup-slopes and sub-solutions for fully nonlinear elliptic equations},
author = {Bin Guo and Jian Song},
journal= {arXiv preprint arXiv:2405.03074},
year = {2024}
}