Surface families and boundary behavior of quasiregular mappings (Q819230)

The author studies the boundary behavior of bounded quasiregular mappings \(f:B^n(0,1)\to \mathbb{R}^n\), \(n\geq 3\). After a brief, informative review of related results, he states his theorem: There is a large family of cones (or more general cone-like sets) in the unit ball with vertices on the boundary sphere such that their images under \(f\) have finite \((n-1)\)-dimensional Hausdorff measure. The main tool in the proof is the conformal modulus of a family of \((n-1)\)-dimensional surfaces.