Fully non-linear elliptic equations on compact Hermitian manifolds
Differential Geometry
2015-04-24 v3
Abstract
We derive a priori estimates for solutions of a general class of fully non-linear equations on compact Hermitian manifolds. Our method is based on ideas that have been used for different specific equations, such as the complex Monge-Amp\`ere, Hessian and inverse Hessian equations. As an application we solve a class of Hessian quotient equations on K\"ahler manifolds assuming the existence of a suitable subsolution. The method also applies to analogous equations on compact Riemannian manifolds.
Cite
@article{arxiv.1501.02762,
title = {Fully non-linear elliptic equations on compact Hermitian manifolds},
author = {Gábor Székelyhidi},
journal= {arXiv preprint arXiv:1501.02762},
year = {2015}
}
Comments
v3: minor corrections, v2: 34 pages, added references, examples, minor corrections