Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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.

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Article copyright: © Copyright 1993 American Mathematical Society