De Lellis, C; Müller, S (2006). A C⁰ estimate for nearly umbilical surfaces. Calculus of Variations and Partial Differential Equations, 26(3):283-296.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Analysis
Physical Sciences > Applied Mathematics |
| Language: | English |
| Date: | 2006 |
| Deposited On: | 12 Jan 2010 11:14 |
| Last Modified: | 30 Jun 2022 04:11 |
| Publisher: | Springer |
| ISSN: | 0944-2669 |
| Additional Information: | The original publication is available at www.springerlink.com |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1007/s00526-006-0005-5 |
De Lellis, C