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Hypersurfaces with constant mean curvature in hyperbolic space form

✍ Scribed by Jean-Marie Morvan; Wo Bao-Qiang

Publisher
Springer
Year
1996
Tongue
English
Weight
895 KB
Volume
59
Category
Article
ISSN
0046-5755

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✦ Synopsis

In this article, we prove the following theorem: A complete hypersurface of the hyperbolic space form, which has constant mean curvature and non-negative Ricci curvature Q, has non-negative sectional curvature. Moreover, if it is compact, it is a geodesic distance sphere; if its soul is not reduced to a point, it is a geodesic hypercylinder; if its soul is reduced to a point p, its curvature satisfies NvQII < o0, and the geodesic spheres centered at p are convex, then it is a horosphere.

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