Sobolev homeomorphisms and Brennan's conjecture

Vladimir Gol'dshtein, Alexander Ukhlov

Let $\Omega \subset {\mathbb{R}}^n$ be a domain that supports the $p$-Poincaré inequality. Given a homeomorphism $\phi \in L_p^1(\Omega )$, for $p>n$ we show the domain $\phi (\Omega )$ has finite geodesic di…