A note on a rigidity estimate for degree $\pm 1$ conformal maps on ${\mathbb{S}}^2$

Abstract

In this note we present a short alternative proof of an estimate obtained by A.B.-Mantel, C.B. Muratov and T.M. Simon in [3] regarding the rigidity of degree {$\pm 1$} conformal maps of ${\mathbb{S}}^2$, i.e. its Möbius transformations.

7 pages