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arXiv · 1504.07419

A Hopf theorem for non-constant mean curvature and a conjecture of A.D. Alexandrov

Jose A. Galvez·Pablo Mira
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Abstract

We prove a uniqueness theorem for immersed spheres of prescribed (non-constant) mean curvature in homogeneous three-manifolds. In particular, this uniqueness theorem proves a conjecture by A.D. Alexandrov about immersed spheres of prescribed Weingarten curvature in R3 for the special but important case of prescribed mean curvature. As a consequence, we extend the classical Hopf uniqueness theorem for constant mean curvature spheres to the case of immersed spheres of prescribed antipodally symmetric mean curvature in R3.

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Jose A. Galvez, Pablo Mira. 2015-04-28. A Hopf theorem for non-constant mean curvature and a conjecture of A.D. Alexandrov. https://arxiv.org/abs/1504.07419

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