On BLD-mappings with small distortion

Aapo Kauranen, Rami Luisto, Ville Tengvall

We show that every $L$-BLD-mapping in a domain of ${\mathbb{R}}^n$ is a local homeomorphism if $L<\sqrt{2}$ or $K_I(f)<2$. These bounds are sharp as shown by a winding map.