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

Abstract

In this paper, we study 4 4 -dimensional complete hypersurfaces with w w -constant mean curvature in the unit sphere. We give a lower bound of the scalar curvature for 4 4 -dimensional complete hypersurfaces with w w -constant mean curvature. As a by-product, we give a new proof of the result of Deng-Gu-Wei [Adv. Math. 314 (2017), pp. 278–305] under the weaker topological condition.