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Index Growth of hypersurfaces with constant mean curvature

Pierre Bérard·Levi Lopes de Lima·Wayne Rossman
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Abstract

In this paper we give the precise index growth for the embedded hypersurfaces of revolution with constant mean curvature (cmc) 1 in $\R^{n}$ (Delaunay unduloids). When $n=3$, using the asymptotics result of Korevaar, Kusner and Solomon, we derive an explicit asymptotic index growth rate for finite topology cmc 1 surfaces with properly embedded ends. Similar results are obtained for hypersurfaces with cmc bigger than 1 in hyperbolic space.

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Pierre Bérard, Levi Lopes de Lima, Wayne Rossman. 2000-11-07. Index Growth of hypersurfaces with constant mean curvature. https://arxiv.org/abs/math/0011039

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