Abstract
The main results of this chapter are a Picard-type theorem (Theorem 2.1) on omitted values and its variants. In dimension three it is known that this result is qualitatively best possible (Theorem 2.2). The proof of 2.2 is very technical and will not be presented here. We merely refer the reader to the article [R11]. In Section 3 we will give a quantitative growth estimate for mappings of the unit ball into the n-sphere with punctures, which delivers as a special case a counterpart to the Picard-Schottky theorem of classical function theory.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Rickman, S. (1993). Mappings into the n-Sphere with Punctures. In: Quasiregular Mappings. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78201-5_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-78201-5_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-78203-9
Online ISBN: 978-3-642-78201-5
eBook Packages: Springer Book Archive