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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