Optimal quantitative stability of the Möbius group of the sphere in all dimensions

André Guerra, Xavier Lamy, Konstantinos Zemas

In any dimension $n\ge 3$, we prove an optimal stability estimate for the Möbius group among maps $u:{\mathbb{S}}^{n-1}\to {\mathbb{R}}^n$, of the form $\inf_{λ>0,ϕ\in \mathrm{Mö…