Index growth of hypersurfaces with constant mean curvature |
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| Authors: | Pierre Bérard Levi Lopes de Lima Wayne Rossman |
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| Institution: | (1) Institut Fourier, UMR 5582 UJF–CNRS, Université Joseph Fourier, B.P. 74, 38402 St Martin d'Hères Cedex, France (e-mail: Pierre.Berard@ujf-grenoble.fr / http://www-fourier.ujf-grenoble.fr/, FR;(2) Departamento de Matemática, Universidade Federal do Ceará, Campus do Pici, 60455–760 Fortaleza, Brazil (e-mail: levi@mat.ufc.br), BR;(3) Department of Mathematics, Faculty of Science, Kobe University, Rokko, Kobe 657-8501, Japan (e-mail. wayne@math.kobe-u.ac.jp / http://www.math.kobe-u.ac.jp/HOME/wayne/wayne.html), JP |
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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 (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.
Received: 6 July 2000; in final form: 10 September 2000 / Published online: 25 June 2001 |
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| Keywords: | Mathematics Subject Classification (2000): 53A10 53A35 |
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