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arXiv · 1405.7335

Quantitative rigidity results for conformal immersions

Tobias Lamm·Huy The Nguyen
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Abstract

In this paper we prove several quantitative rigidity results for conformal immersions of surfaces in $\mathbb{R}^n$ with bounded total curvature. We show that (branched) conformal immersions which are close in energy to either a round sphere, a conformal Clifford torus, an inverted catenoid, an inverted Enneper's minimal surface or an inverted Chen's minimal graph must be close to these surfaces in the $W^{2,2}$-norm. Moreover, we apply these results to prove a corresponding rigidity result for complete, connected and non-compact surfaces.

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Tobias Lamm, Huy The Nguyen. 2014-05-28. Quantitative rigidity results for conformal immersions. https://arxiv.org/abs/1405.7335

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