AC0Estimate for Nearly Umbilical Surfaces

✍ Scribed by Camillo De Lellis; Stefan Müller

• Book ID: 106176061
• Publisher: Springer
• Year: 2006
• Tongue: English
• Weight: 319 KB
• Volume: 26
• Category: Article
• ISSN: 0944-2669
• DOI: 10.1007/s00526-006-0005-5

✦ Synopsis

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