Stability of Hypersurfaces with Constant Mean Curvature

Abstract

Let $$x:{\text M}^{n}\rightarrow\,{\text R}^{n+1}$$be an immersion of an orientable, n-dimensional manifold $${\text M}^{n}$$into the euclidean space $${\text R}^{n+1}$$. The condition that x has nonzero constant mean curvature H = H0 is known to be equivalent to the fact that xis a critical point of a variational problem.