Index Growth of hypersurfaces with constant mean curvature

Details Index Growth of hypersurfaces with constant mean curvature Index Growth of hypersurfaces with constant mean curvature

2000-11-07

arxiv.org/abs/math/0011039v1

Math. Zeit. 239 (2002), 99-115

Mathematics

Differential Geometry

13 pages, to appear in Mathematische Zeitschrift

Scientific paper

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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