Stability estimates for the conformal group of $\mathbb{S}^{n-1}$ in dimension $n\geq 3$

Stephan Luckhaus; Konstantinos Zemas

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arXiv · 1910.01862

Stability estimates for the conformal group of $\mathbb{S}^{n-1}$ in dimension $n\geq 3$

Stephan Luckhaus·Konstantinos Zemas

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Abstract

The purpose of this paper is to exhibit a quantitative stability result for the class of M\"obius transformations of $\mathbb{S}^{n-1}$ when $n\geq 3$. The main estimate is of local nature and asserts that for a Lipschitz map that is apriori close to a M\"obius transformation, an average conformal-isoperimetric type of deficit controls the deviation (in an average sense) of the map in question from a particular M\"obius map. The optimality of the result together with its link with the geometric rigidity of the special orthogonal group are also discussed.

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BibTeX RIS

Stephan Luckhaus, Konstantinos Zemas. 2019-10-04. Stability estimates for the conformal group of $\mathbb{S}^{n-1}$ in dimension $n\geq 3$. https://arxiv.org/abs/1910.01862

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