Index and total curvature of surfaces with constant mean curvature

Manfredo P. do Carmo, Alexandre M. Da Silveira
1990 Proceedings of the American Mathematical Society  
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