# 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.

## 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.

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## Additional indexing

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Physical Sciences > Analysis Physical Sciences > Applied Mathematics English 2006 12 Jan 2010 11:14 29 Jul 2020 19:35 Springer 0944-2669 The original publication is available at www.springerlink.com Green https://doi.org/10.1007/s00526-006-0005-5

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