Linear dilatation and differentiability of homeomorphisms of $\mathbb{R}^{n}$
Linear dilatation and differentiability of homeomorphisms of $\mathbb{R}^{n}$
According to a classical result, if $\Omega$ is a domain in $\mathbb {R}^d$, where $d>1$, $f: \Omega \rightarrow \mathbb {R}^d$ is a homeomorphism and the lim-sup dilatation $H_f$ of $f$ is finite almost everywhere on $\Omega$, then $f$ is differentiable almost everywhere on $\Omega$. We show that this theorem fails …