Rigidity estimates for isometric and conformal maps from ${\mathbb{S}}^{n-1}$ to ${\mathbb{R}}^n$

Stephan Luckhaus, Konstantinos Zemas

We investigate both linear and nonlinear stability aspects of rigid motions (resp. Möbius transformations) of ${\mathbb{S}}^{n-1}$ among Sobolev maps from ${\mathbb{S}}^{n-1}$ into $\m…