Generic properties of critical points of the boundary mean curvature

Abstract

Given a bounded domain $\Omega\subset\mathbb{R}^N$ of class $C^k$ with $k\ge3$, we prove that for a generic deformation $I+\psi$, with $\psi$ small enough, all the critical points of the mean curvature of the boundary of the domain $(I+\psi)\Omega$ are non degenerate.