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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Index and total curvature of surfaces with constant mean curvature


Authors: Manfredo P. do Carmo and Alexandre M. Da Silveira
Journal: Proc. Amer. Math. Soc. 110 (1990), 1009-1015
MSC: Primary 53C42; Secondary 53A10, 58G30
MathSciNet review: 1039255
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Abstract: We prove an analogue, for surfaces with constant mean curvature in hyperbolic space, of a theorem of Fischer-Colbrie and Gulliver about minimal surfaces in Euclidean space. That is, for a complete surface $ {M^2}$ in hyperbolic $ 3$-space with constant mean curvature 1, the (Morse) index of the operator $ L = \Delta - 2K$ is finite if and only if the total Gaussian curvature is finite.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1039255-5
PII: S 0002-9939(1990)1039255-5
Article copyright: © Copyright 1990 American Mathematical Society