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A C⁰ estimate for nearly umbilical surfaces


De Lellis, C; Müller, S (2006). A C⁰ estimate for nearly umbilical surfaces. Calculus of Variations and Partial Differential Equations, 26(3):283-296.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2006
Deposited On:12 Jan 2010 11:14
Last Modified:05 Apr 2016 13:24
Publisher:Springer
ISSN:0944-2669
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s00526-006-0005-5
Permanent URL: https://doi.org/10.5167/uzh-21623

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