The r-mean curvature and rigidity of compact hypersurfaces in the Euclidean space

TL;DR

This paper characterizes round spheres in Euclidean space by examining conditions on the r-mean curvature, providing new insights into the rigidity of compact hypersurfaces.

Contribution

It introduces new conditions on r-mean curvature that uniquely identify round spheres among compact hypersurfaces in Euclidean space.

Findings

Round spheres are characterized by specific r-mean curvature conditions.

New rigidity results for compact hypersurfaces based on r-mean curvature.

Conditions under which hypersurfaces are necessarily spherical.

Abstract

In this paper, we characterize round spheres in the Euclidean space under some suitable conditions on the r-mean curvature.