A Minkowski type inequality with free boundary in space forms

TL;DR

This paper extends Minkowski inequalities to domains with free boundary conditions on umbilical hypersurfaces in space forms, generalizing previous results and establishing an optimal weighted version.

Contribution

It introduces a Minkowski inequality for free boundary domains on umbilical hypersurfaces in space forms, generalizing prior work to include free boundary cases.

Findings

Established a Minkowski inequality for free boundary domains in space forms.

Generalized previous Minkowski inequalities to free boundary settings.

Derived an optimal weighted Minkowski inequality in this context.

Abstract

In this paper, we consider a Minkowski inequality for a domain supported on any umbilical hypersurface with free boundary in space forms. We generalize the main result in \cite{Xia} into free boundary case and obtain a free boundary version of optimal weighted Minkowski inequality in space forms.