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arXiv · 1902.09405

Rotational hypersurfaces of prescribed mean curvature

Antonio Bueno·Jose A. Galvez·Pablo Mira
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Abstract

We use a phase space analysis to give some classification results for rotational hypersurfaces in $\mathbb{R}^{n+1}$ whose mean curvature is given as a prescribed function of its Gauss map. For the case where the prescribed function is an even function in $\mathbb{S}^n$, we show that a Delaunay-type classification holds for this class of hypersurfaces. We also exhibit examples showing that the behavior of rotational hypersurfaces of prescribed (non-constant) mean curvature is much richer than in the constant mean curvature case.

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Antonio Bueno, Jose A. Galvez, Pablo Mira. 2019-02-25. Rotational hypersurfaces of prescribed mean curvature. https://arxiv.org/abs/1902.09405

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