Published Paper
Inserted: 8 mar 2005
Last Updated: 3 may 2011
Journal: Calc. Var. Partial Differential Equations
Volume: 26
Number: 3
Pages: 283-296
Year: 2006
Abstract:
Let $\Sigma$ be a smooth
compact connected surface of $*R*^3$ without
boundary and denote by $A$ its second fundamental.
In a previous paper we proved that, if $\
A- ({\rm tr } A/2) {\rm Id}\
_{L^2 (\Sigma)}$ is small, then
$\Sigma$ is $W^{2,2}$--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 $*S*^2$.
For the most updated version and eventual errata see the page
http:/www.math.uzh.chindex.php?id=publikationen&key1=493
Keywords: rigidity, second fundamental form, umbilical surfaces