Stable hypersurfaces with constant higher order mean curvature

TL;DR

This paper introduces a new stability concept for capillary hypersurfaces with constant higher order mean curvature and extends classical stability results to this broader setting.

Contribution

It generalizes classical stability theory to include hypersurfaces with higher order mean curvature and capillary boundary conditions.

Findings

Defined a new stability notion for these hypersurfaces

Extended classical stability results to higher order mean curvature cases

Provides theoretical framework for future research in geometric analysis

Abstract

We propose a notion of stability for capillary hypersurfaces with constant higher order mean curvature and we generalize some results of the classical stability theory for CMC capillary hypersurfaces.