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Hypersurfaces of constant mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity

✍ Scribed by Guan, Bo; Spruck, Joel

Book ID
118226226
Publisher
John Hopkins University Press
Year
2000
Tongue
English
Weight
243 KB
Volume
122
Category
Article
ISSN
0002-9327

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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

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We study compact spacelike hypersurfaces (necessarily with non-empty boundary) with constant mean curvature in the (n + 1)-dimensional Lorentz-Minkowski space. In particular, when the boundary is a round sphere we prove that the only such hypersurfaces are the hyperplanar round balls (with zero mean