## Illinois Journal of Mathematics

### Surface families and boundary behavior of quasiregular mappings

Kai Rajala

#### 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.

#### Article information

Source
Illinois J. Math., Volume 49, Number 4 (2005), 1145-1153.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138131

Digital Object Identifier
doi:10.1215/ijm/1258138131

Mathematical Reviews number (MathSciNet)
MR2210356

Zentralblatt MATH identifier
1089.30018

Subjects
Primary: 30C65: Quasiconformal mappings in $R^n$ , other generalizations

#### Citation

Rajala, Kai. Surface families and boundary behavior of quasiregular mappings. Illinois J. Math. 49 (2005), no. 4, 1145--1153. doi:10.1215/ijm/1258138131. https://projecteuclid.org/euclid.ijm/1258138131