Fully nonlinear elliptic equations on Hermitian manifolds for symmetric functions of partial Laplacians
Analysis of PDEs
2021-10-04 v1 Complex Variables
Differential Geometry
Abstract
We consider a class of fully nonlinear second order elliptic equations on Hermitian manifolds closely related to the general notion of -plurisubharmonicity of Harvey-Lawson and an equation treated by Sz\'ekelyhidi-Tosatti-Weinkove in the proof of Gauduchon conjecture. Under fairly general assumptions we derive interior estimates and establish the existence of smooth solutions for the Dirichlet problem as well as for equations on closed manifolds.
Keywords
Cite
@article{arxiv.2110.00490,
title = {Fully nonlinear elliptic equations on Hermitian manifolds for symmetric functions of partial Laplacians},
author = {Mathew George and Bo Guan and Chunhui Qiu},
journal= {arXiv preprint arXiv:2110.00490},
year = {2021}
}