Complete hypersurfaces with $w$-constant mean curvature in the unit spheres

TL;DR

This paper investigates 4-dimensional complete hypersurfaces with constant weighted mean curvature in the unit sphere, establishing scalar curvature bounds and providing a new proof of existing results under weaker topological assumptions.

Contribution

It offers a lower bound for scalar curvature of such hypersurfaces and presents a novel proof of Deng-Gu-Wei's result with relaxed topological conditions.

Findings

Established a scalar curvature lower bound for 4D hypersurfaces with w-constant mean curvature.

Provided a new proof of Deng-Gu-Wei's theorem under weaker topological assumptions.

Enhanced understanding of geometric properties of hypersurfaces in spheres.

Abstract

In this paper, we study $4$-dimensional complete hypersurfaces with $w$-constant mean curvature in the unit sphere. We give a lower bound of the scalar curvature for $4$-dimensional complete hypersurfaces with $w$-constant mean curvature. As a by-product, we give a new proof of the result of Deng-Gu-Wei under the weaker topological condition.