Surface families and boundary behavior of quasiregular mappings

Abstract

We study the boundary behavior of bounded quasiregular mappings $f: B^n(0,1)\to \rn$, $n \geq 3$. We show that there exists a large family of cusps, with vertices on the boundary sphere $S^{n-1}(0,1)$, so that the images of these cusps under $f$ have finite $(n-1)$-measure.