Nondegeneracy of critical points of the mean curvature of the boundary for Riemannian manifolds

Abstract

Let $M$ be a compact smooth Riemannian manifold of finite dimension $n+1$ with boundary $\partial M$and $\partial M$ is a compact $n$-dimensional submanifold of $M$. We show that for generic Riemannian metric $g$, all the critical points of the mean curvature of $\partial M$ are nondegenerate.

References in corpus (1)

• Positive solutions of singularly perturbed nonlinear elliptic problem on Riemannian manifolds with boundary