Sphere-foliated minimal and constant mean curvature hypersurfaces in product spaces

Abstract

In this paper, we prove that minimal hypersurfaces when $n\ge 3$ and nonzero constant mean curvature hypersurfaces when $n\ge 2$ foliated by spheres in parallel horizontal hyperplanes in ${\mathbb{H}}^n\times \mathbb{R}$ must be rotationally symmetric.

arXiv commentThis article is to appear in Bull. Korean Math. Soc. in 2010

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