Sharpness of Rickman’s Picard theorem in all dimensions

David Drasin; Pekka Pankka

doi:10.1007/s11511-015-0125-x

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Home > Journals > Acta Math. > Volume 214 > Issue 2 > Article

2015 Sharpness of Rickman’s Picard theorem in all dimensions

David Drasin, Pekka Pankka

Author Affiliations +

David Drasin,¹ Pekka Pankka²
¹Department of Mathematics, Purdue University
²Department of Mathematics and Statistics; Department of Mathematics and Statistics

Acta Math. 214(2): 209-306 (2015). DOI: 10.1007/s11511-015-0125-x

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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 ${y_1, \ldots, y_q}$ .

Funding Statement

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

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David Drasin. Pekka Pankka. "Sharpness of Rickman’s Picard theorem in all dimensions." Acta Math. 214 (2) 209 - 306, 2015. https://doi.org/10.1007/s11511-015-0125-x