Foliations by constant mean curvature tubes

Rafe Mazzeo; Frank Pacard

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Foliations by constant mean curvature tubes

Rafe Mazzeo·Frank Pacard

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Abstract

Let $Γ$ be a nondegenerate geodesic in a compact Riemannian manifold $M$. We prove the existence of a partial foliation of a neighbourhood of $Γ$ by CMC surfaces which are small perturbations of the geodesic tubes about $Γ$. There are gaps in this foliation, which correspond to a bifurcation phenomenon. Conversely, we also prove, under certain restrictions, that the existence of a partial CMC foliation of this type about a submanifold $Γ$ of any dimension implies that $Γ$ is minimal.

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BibTeX RIS

Rafe Mazzeo, Frank Pacard. 2003-08-05. Foliations by constant mean curvature tubes. https://arxiv.org/abs/math/0308044

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