A Harnack-Type Inequality for a Prescribing Curvature equation on a Domain with Boundary

TL;DR

This paper establishes a Harnack-type inequality for prescribing curvature equations on domains with boundary, providing key energy estimates under specific curvature conditions.

Contribution

It introduces a min-max inequality and energy estimates for prescribing curvature equations on half Euclidean balls, advancing understanding of boundary value problems in geometric analysis.

Findings

Proved a Harnack-type inequality for curvature equations.

Established energy estimates under curvature assumptions.

Developed a min-max inequality for boundary domains.

Abstract

In this paper we consider a class of prescribing curvature type equations on half Euclidean balls. Under suitable assumptions on the scalar curvature function and boundary mean curvature function we prove a min-max type inequality and the corresponding energy estimates.