Regularity of fully non-linear elliptic equations on Hermitian manifolds. III

TL;DR

This paper establishes boundary estimates and proves the existence of solutions for a class of fully nonlinear elliptic equations on Hermitian manifolds under near-optimal structural conditions.

Contribution

It provides a quantitative boundary estimate and existence results for nonlinear elliptic equations on Hermitian manifolds, advancing the understanding of such equations in complex geometry.

Findings

Derived a quantitative boundary estimate.

Proved existence of solutions to Dirichlet problem.

Applicable under almost optimal structural conditions.

Abstract

Under structural conditions which are almost optimal, we derive a quantitative version of boundary estimate then prove existence of solutions to Dirichlet problem for a class of fully nonlinear elliptic equations on Hermitian manifolds.