Rotational hypersurfaces of prescribed mean curvature

2019/02/25 by Bueno, Antonio, Galvez, Jose A., Mira, Pablo
#34C05 #34C40 #53A10 #53C42 #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.09405

Abstract

We use a phase space analysis to give some classification results for rotational hypersurfaces in ℝⁿ⁺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 \mathbbSⁿ, 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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