Optimal rigidity estimates for maps of a compact Riemannian manifold to itself

Sergio Conti, Georg Dolzmann, Stefan Müller

Let $M$ be a smooth, compact, connected, oriented Riemannian manifold, and let $ı:M\to {\mathbb{R}}^d$ be an isometric embedding. We show that a Sobolev map $f:M\to M$ which…