Foliation by constant mean curvature spheres (Q756151)

The author summarizes the paper as follows: Let M be a Riemannian manifold of dimension \(n+1\) and \(p\in M\). Geodesic spheres around p of small radius constitute a smooth foliation. We shall show that this foliation can be perturbed into a foliation whose leaves are spheres of constant mean curvature, provided that p is a nondegenerate critical point of the scalar curvature function of M. The obtained foliation is actually the unique foliation by constant mean curvature hypersurfaces which is regularly centered at p. On the other hand, if p is not a critical point of the scalar curvature function, then there exists no such foliation.