Viscosity solution to complex Hessian equations on compact Hermitian manifolds
Analysis of PDEs
2025-01-27 v2 Differential Geometry
Abstract
We prove the existence of viscosity solutions to complex Hessian equations on a compact Hermitian manifold that satisfy a determinant domination condition. This viscosity solution is shown to be unique when the right hand is strictly monotone increasing in terms of the solution. When the right hand side does not depend on the solution, we reduces it to the strict monotonicity of the solvability constant.
Keywords
Cite
@article{arxiv.2406.00953,
title = {Viscosity solution to complex Hessian equations on compact Hermitian manifolds},
author = {Jingrui Cheng and Yulun Xu},
journal= {arXiv preprint arXiv:2406.00953},
year = {2025}
}