## Acta Mathematica

### Sharpness of Rickman’s Picard theorem in all dimensions

#### Abstract

We show that given ${n \geqslant 3}$, ${q \geqslant 1}$, and a finite set ${\{y_1, \ldots, y_q \}}$ in ${\mathbb{R}^n}$ there exists a quasiregular mapping ${\mathbb{R}^n\to \mathbb{R}^n}$ omitting exactly points ${y_1, \ldots, y_q}$.

#### Note

P.P. was partly supported by NSF grant DMS-0757732 and the Academy of Finland projects 126836 and 256228.

#### Article information

Source
Acta Math., Volume 214, Number 2 (2015), 209-306.

Dates
Received: 28 April 2013
Revised: 13 November 2014
First available in Project Euclid: 30 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485802422

Digital Object Identifier
doi:10.1007/s11511-015-0125-x

Mathematical Reviews number (MathSciNet)
MR3372169

Zentralblatt MATH identifier
1326.30025

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

Rights
2015 © Institut Mittag-Leffler

#### Citation

Drasin, David; Pankka, Pekka. Sharpness of Rickman’s Picard theorem in all dimensions. Acta Math. 214 (2015), no. 2, 209--306. doi:10.1007/s11511-015-0125-x. https://projecteuclid.org/euclid.acta/1485802422

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