For hypersurfaces with mean curvature H = ⟨η, v⟩ + λ, the paper gives explicit parametrizations of cylindrical flat examples and a complete classification of rotational examples.
Rotational hypersurfaces of prescribed mean curvature
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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.
fields
math.DG 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Invariant hypersurfaces with linear prescribed mean curvature
For hypersurfaces with mean curvature H = ⟨η, v⟩ + λ, the paper gives explicit parametrizations of cylindrical flat examples and a complete classification of rotational examples.