A lower bound for areas of the rotational hypersurfaces with 𝐻ₘ=0 in the spheres

Abstract

In this paper, we study the areas of compact rotational hypersurfaces with H m = 0 H_m=0 in the spheres, prove that the set for areas of these hypersurfaces is a discrete set and obtain a lower bound for this set, where H m H_m is the m m -th mean curvature of the hypersurface.