Convexity of Hessian Integrals and Poincare Type Inequalities

TL;DR

This paper investigates integrals involving Hessian operators in real and complex settings, establishing Poincare inequalities that extend earlier results by Trudinger and Wang.

Contribution

It introduces generalized Poincare inequalities for Hessian integrals in both real and complex domains, expanding the theoretical framework.

Findings

Proved Poincare type inequalities for Hessian integrals

Extended earlier results of Trudinger and Wang

Established convexity properties of Hessian integrals

Abstract

In this paper, we studied integrals involving both real and complex Hessian operators over bounded domain. Poincare type inequalities were proved in both cases which generalized a early results of Trudinger and Wang.