• 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}
}

• S. Luckhaus, Konstantinos Zemas
• 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 rigidity of the special orthogonal group are also discussed.