Second order estimates for $\chi$-semi convex solutions of Hessian equations on Hermitian manifolds
Analysis of PDEs
2025-07-21 v2
Abstract
In this paper, we establish the modified concavity inequality for complex Hessian equations under the semi-convexity assumption inspired by Lu \cite{Lu23} and Zhang \cite{Z24} for real case. Then second order estimates for admissible solutions of complex Hessian equations on compact Hermitian manifolds with both sides of equations depending on gradient terms are obtained by taking advantage of the crucial inequality.
Keywords
Cite
@article{arxiv.2501.01017,
title = {Second order estimates for $\chi$-semi convex solutions of Hessian equations on Hermitian manifolds},
author = {Xiaojuan Chen and Qiang Tu and Ni Xiang},
journal= {arXiv preprint arXiv:2501.01017},
year = {2025}
}