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arXiv · 1408.2089

Rigidity and non-rigidity results for conformal immersions

Tobias Lamm·Reiner M. Schätzle
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Abstract

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].

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Tobias Lamm, Reiner M. Schätzle. 2014-08-09. Rigidity and non-rigidity results for conformal immersions. https://arxiv.org/abs/1408.2089

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