A C0 estimate for nearly umbilical surfaces

被引:34
作者
De Lellis, C [1 ]
Müller, S [1 ]
机构
[1] Max Planck Inst Math Sci, D-04103 Leipzig, Germany
关键词
D O I
10.1007/s00526-006-0005-5
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let Sigma subset of R-3 be a smooth compact connected surface without boundary. Denote by A its second fundamental form and by angstrom the tensor A - ( tr A/2) Id. In [ 4] we proved that, if parallel to angstrom parallel to(L2(Sigma)) is small, then Sigma is W-2,W-2-close to a round sphere. In this note we show that, in addition, the metric of Sigma is C-0-close to the standard metric of S-2.
引用
收藏
页码:283 / 296
页数:14
相关论文
共 4 条
[1]  
COIFMAN R, 1993, J MATH PURE APPL, V72, P247
[2]  
DELELLIS C, IN PRESS J DIFF GEOM
[3]  
Fefferman C, 1972, ACTA MATH-DJURSHOLM, V129, P137, DOI 10.1007/BF02392215
[4]  
Muller S, 1995, J DIFFER GEOM, V42, P229