Title | A $C^0$ estimate for nearly umbilical surfaces. |

Publication Type | Journal Article |

Year of Publication | 2006 |

Authors | De Lellis C., Müller S. |

Journal | Calculus of Variations and Partial Differential Equations |

Volume | 26 |

Pagination | 283–296 |

Publisher | Springer |

Type of Article | differential geometry |

ISSN | 0944-2669 |

Abstract | Let \ensuremathΣ ? 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 (\ensuremathΣ) is small, then \ensuremathΣ is W 2,2-close to a round sphere. In this note we show that, in addition, the metric of \ensuremathΣ is C 0?close to the standard metric of S 2. |

Notes | Calc. Var. Partial Differential Equations 26 (2006), no. 3, 283–296. |

URL | http://www.springerlink.com/content/ww16r1w618538614/ |

DOI | 10.1007/s00526-006-0005-5 |

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