Concavity-Free $L^{\infty }$ Estimates and Stability for Fully Nonlinear Complex Equations

Abstract

In this paper, we extend the $L^{\infty }$ estimates of Guo-Phong for fully non-linear equations on compact hermitian manifolds to a possibly indefinite reference form satisfying a uniform admissibility criterion. Furthermore, we also establish one-sided stability estimates. Neither result requires homogeneity or concavity of the nonlinear operator.

arXiv comment15 pages, comments welcome