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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 itsarrive perpendicular to the boundary of M, provided that $p$ is a nondegeneratecritical point of the mean curvature function of $\partial M$.

Foliation by free boundary constant mean curvature leaves