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Transactions of the American Mathematical Society

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Hypersurfaces with constant mean curvature in the complex hyperbolic space

Authors: Susana Fornari, Katia Frensel and Jaime Ripoll
Journal: Trans. Amer. Math. Soc. 339 (1993), 685-702
MSC: Primary 53C42; Secondary 53C40
Erratum: Trans. Amer. Math. Soc. 347 (1995), null.
MathSciNet review: 1123452
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Abstract: A classical theorem of A. D. Alexandrov characterized round spheres is extended to the complex hyperbolic space $ {\mathbf{C}}{{\mathbf{H}}^2}$ of constant holomorphic sectional curvature. A detailed description of the horospheres and equidistant hypersurfaces in $ {\mathbf{C}}{{\mathbf{H}}^2}$ determining in particular their stability, is also given.

References [Enhancements On Off] (What's this?)

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  • [BdoCE] J. L. Barbosa, M. P. do Carmo, and J. Eschenburg, Stability of hypersurfaces with constant mean curvature in Riemannian manifolds, Math. Z. 197 (1988), 124-138. MR 917854 (88m:53109)
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