• DOI:10.5167/UZH-21623
• Corpus ID: 125403037

A C⁰ estimate for nearly umbilical surfaces

@inproceedings{DeLellis2006ACE,
  title={A C⁰ estimate for nearly umbilical surfaces},
  author={Camillo De Lellis and Stefan M{\"u}ller},
  year={2006},
  url={https://api.semanticscholar.org/CorpusID:125403037}
}

• Camillo De Lellis, S. Müller
• Published 2006
• Mathematics

Let Σ ⊂ R 3 be a smooth compact connected surface without boundary. Denote by A its second fundamental form and by A the tensor A−(tr A/2)Id. In [4] we proved that, if ‖A‖ 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 A the tensor A−(tr A/2)Id. In [4] we proved that, if ‖A‖ 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.