• Corpus ID: 203737260

# 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}
}```
• Published 4 October 2019
• Mathematics
• arXiv: Differential Geometry
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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