Sharp quantitative stability of the Möbius group among sphere-valued maps in arbitrary dimension

André Guerra, Xavier Lamy, Konstantinos Zemas

In this work we prove a sharp quantitative form of Liouville's theorem, which asserts that, for all $n\ge 3$, the weakly conformal maps of ${\mathbb{S}}^{n-1}$ with degree $\pm 1$ ar…