Mathematische Zeitschrift

, Volume 239, Issue 1, pp 99–115 | Cite as

Index growth of hypersurfaces with constant mean curvature

  • Pierre Bérard
  • Levi Lopes de Lima
  • Wayne Rossman
Original article

Abstract.

In this paper we give the precise index growth for the embedded hypersurfaces of revolution with constant mean curvature (cmc) 1 in \(\mathbb{R}^n\) (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.

Mathematics Subject Classification (2000): 53A10, 53A35 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Pierre Bérard
    • 1
  • Levi Lopes de Lima
    • 2
  • Wayne Rossman
    • 3
  1. 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. 2.Departamento de Matemática, Universidade Federal do Ceará, Campus do Pici, 60455–760 Fortaleza, Brazil (e-mail: levi@mat.ufc.br)BR
  3. 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

Personalised recommendations