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arXiv · 2302.09809

Small spheres with prescribed nonconstant mean curvature in Riemannian manifolds

Alberto Enciso·Antonio J. Fernández·Daniel Peralta-Salas
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Abstract

Given a function $f$ on a smooth Riemannian manifold without boundary, we prove that if $p \in M$ is a non-degenerate critical point of $f$, then a neighborhood of $p$ contains a foliation by spheres with mean curvature proportional to $f$. This foliation is essentially unique. The nondegeneracy assumption can be substantially relaxed, at the expense of losing the property that the family of spheres with prescribed mean curvature defines a foliation.

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Alberto Enciso, Antonio J. Fernández, Daniel Peralta-Salas. 2023-02-20. Small spheres with prescribed nonconstant mean curvature in Riemannian manifolds. https://arxiv.org/abs/2302.09809

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