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A C 0 Estimate for Nearly Umbilical Surfaces

  • Camillo De Lellis
  • Stefan MüllerEmail author
Article

Abstract

Let Σ ⊂ R 3 be a smooth compact connected surface without boundary. Denote by A its second fundamental form and by Å the tensor A−(tr A/2)Id. In [4] we proved that, if ‖Å L 2 (Σ) is small, then Σ is W 2,2-close to a round sphere. In this note we show that, in addition, the metric of Σ is C 0–close to the standard metric of S 2.

Keywords

Hardy Space Fundamental Form Universal Constant Beltrami Operator Round Sphere 
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References

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    Müller, S., Šverák, V.: On surfaces of finite total curvature, J. Diff. Geom. 42(2), 229–258 (1995)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Max–Planck Institute for Mathematics in the SciencesLeipzigGermany

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