Radius estimates for nearly stable H-hypersurfaces of dimension 2, 3, and 4

Abstract

In this paper we study the geometry of complete constant mean curvature (CMC) hypersurfaces immersed in an (n + 1)-dimensional Riemannian manifold N (n = 2, 3 and 4) with sectional curvatures uniformly bounded from below. We generalise radius estimates given by Rosenberg [32] (n = 2) and by Elbert, Nelli and Rosenberg [13] and Cheng [2] (n = 3, 4) to nearly stable CMC hypersurfaces immersed in N. We also prove that certain CMC hypersurfaces effectively embedded in N must be proper.