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

@article{Luckhaus2019StabilityEF, title={Stability estimates for the conformal group of \$\mathbb\{S\}^\{n-1\}\$ in dimension \$n\geq 3\$}, author={Stephan Luckhaus and Konstantinos Zemas}, journal={arXiv: Differential Geometry}, year={2019} }

The purpose of this paper is to exhibit a quantitative stability result for the class of Mobius 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 Mobius transformation, an average conformal-isoperimetric type of deficit controls the deviation (in an average sense) of the map in question from a particular Mobius map. The optimality of the result together with its link with the geometric…

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