Stability estimates for the conformal group of 𝕊n−1 in dimension n ≥ 3
Stephan Luckhaus and Konstantinos Zemas
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Submission date: 04. Oct. 2019
Keywords and phrases: geometric rigidity, stability, Möbius transformations
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The purpose of this paper is to exhibit a quantitative stability result for the class of Möbius transformations of 𝕊n−1 when n ≥ 3. The main estimate is of local nature and asserts that for a Lipschitz map that is apriori close to a Möbius transformation, an average conformal-isoperimetric type of deﬁcit controls the deviation (in an average sense) of the map in question from a particular Möbius map. The optimality of the result together with its link with the geometric rigidity of the special orthogonal group are also discussed.