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Index and total curvature of surfaces with constant mean curvature

1990
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Proceedings of the American Mathematical Society
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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 in hyperbolic 3-space with constant mean curvature 1, the (Morse) index of the operator L = A -2K is finite if and only if the total Gaussian curvature is finite.

doi:10.1090/s0002-9939-1990-1039255-5
fatcat:hyhp23va2vaalpoxppqz2zq3wa