Foliation by free boundary constant mean curvature leaves

Abstract

Let $M$ be a Riemannian manifold of dimension $n+1$ with smooth boundary and $p\in \partial M$. We prove that there exists a smooth foliation around $p$ whose leaves are submanifolds of dimension $n$, constant mean curvature and its arrive perpendicular to the boundary of M, provided that $p$ is a nondegenerate critical point of the mean curvature function of $\partial M$.