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On square integrability of mean curvature for surfaces with positive Gaussian curvature

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Abstract

We show that {ie319-1} H 2dµ = ∞ for any complete surface M ⊂ R 3 which has positive curvature outside a compact subset of R 3. This proves a conjecture of Friedrich.

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References

  • Spivak, M., 1979: A Comprehensive Introduction to Differential Geometry, vol. II. Houston: Publish or Publish.

  • Willmore, T. J., 1967: Note on embedded surfaces, An. Sti. Univ. “Al. l. Cuza”, laşi Sect. Ia Math 11, 493–496.

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Author notes

  1. Marcus Kriele

    Present address: Department of Pure Mathematics, University of Waterloo, N2L3GI, Waterloo, Ontario, Canada

Authors and Affiliations

  1. Fachbereich Mathematik, Ernst-Moritz-Arndt-Universität, Ludwig-Jahn-Str. 15a, O-2200, Greifswald, Bundesrepublik Deutschland

    Ulrich Bunke

  2. Fachbereich Mathematik (Ma 8-3), Technische Universität Berlin, Str. des 17. Juni 136, W-1000, Berlin 12, Bundesrepublik Deutschland

    Marcus Kriele

Authors
  1. Ulrich Bunke
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  2. Marcus Kriele
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Bunke, U., Kriele, M. On square integrability of mean curvature for surfaces with positive Gaussian curvature. Ann Glob Anal Geom 9, 319–324 (1991). https://doi.org/10.1007/BF00136817

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  • DOI: https://doi.org/10.1007/BF00136817

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