Complex Hessian Equation on K\"ahler Manifold

TL;DR

This paper investigates the complex Hessian equation on K"ahler manifolds with non-negative holomorphic bisectional curvature, establishing existence and regularity of solutions under these geometric conditions.

Contribution

It proves the existence and regularity of solutions to the complex Hessian equation on K"ahler manifolds with specific curvature assumptions, advancing understanding in geometric analysis.

Findings

Existence of solutions under non-negative holomorphic bisectional curvature.

Regularity results for solutions to the complex Hessian equation.

Extension of previous results to broader classes of K"ahler manifolds.

Abstract

In this paper, complex Hessian equation over K\"ahler manifold was studied. Under the condition that the underline K\"ahler manifold has non-negative holomorphic bisectional curvature, the existence and regularity of the solution was proved.