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arXiv · 0909.5601

Foliations of Hyperbolic Space by Constant Mean Curvature Hypersurfaces

Baris Coskunuzer
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Abstract

We show that the constant mean curvature hypersurfaces in the hyperbolic n-space spanning the boundary of a star shaped C^{1,1} domain in the asymptotic sphere give a foliation of the hyperbolic n-space. We also show that if C is a closed codimension-1 C^{2,a} submanifold in the asymptotic sphere bounding a unique constant mean curvature hypersurface S_H in the hyperbolic n-space with asymptotic boundary C for any -1<H<1, then the constant mean curvature hypersurfaces {S_H} foliates the hyperbolic n-space.

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Baris Coskunuzer. 2009-09-30. Foliations of Hyperbolic Space by Constant Mean Curvature Hypersurfaces. https://doi.org/10.1093/imrn%2Frnp175

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