%0 Journal Article
%T Rigidity and non-rigidity results for conformal immersions
%A Tobias Lamm
%A Reiner M. Sch£¿tzle
%J Mathematics
%D 2014
%I arXiv
%X In this paper we show a quantitative rigidity result for the minimizer of the Willmore functional among all projective planes in $\mathbb{R}^n$ with $n\ge 4$. We also construct an explicit counterexample to a corresponding rigidity result in codimension one, by showing that an Enneper surface might split-off during a blow-up process. For conformal immersions of spheres with large enough Willmore energies, we construct explicit counterexamples to a quantitative rigidity result and this complements the recently obtained rigidity results in [LaNg13].
%U http://arxiv.org/abs/1408.2089v2