On the Asymptotic Behavior of Quasiconformal Mappings in Space

V. Ya. Gutlyanskiǐ, O. Martio, V. I. Ryazanov and M. Vuorinen
Additional contact information
V. Ya. Gutlyanskiǐ: NAS of Ukraine, Institute of Applied Mathematics and Mechanics
O. Martio: NAS of Ukraine, Institute of Applied Mathematics and Mechanics
V. I. Ryazanov: NAS of Ukraine, Institute of Applied Mathematics and Mechanics
M. Vuorinen: NAS of Ukraine, Institute of Applied Mathematics and Mechanics

A chapter in Quasiconformal Mappings and Analysis, 1998, pp 159-180 from Springer

Abstract: Abstract Conformality at a point of a space quasiconformal mapping is studied without the assumption of differentiability. First, we introduce a notion of asymptotic linearity for general mappings at a prescribed point. Then we prove that the simultaneous asymptotic linearity and analyticity of a mapping f at a point of discreteness imply that f preserves the angles between rays emanating from this point and the moduli of infinitesimal annuli centered at it and thus we strengthen an earlier result of Caraman. Finally, we give sufficient conditions for quasiconformal mappings to be asymptotically linear and analytic in terms of the distortion coefficient and, as a consequence, we generalize the well-known Belinskii weak conformality result to the n-dimensional case.

Keywords: Quasiconformal Mapping; Quasiregular Mapping; Asymptotic Linearity; Distortion Coefficient; Prescribe Point (search for similar items in EconPapers)
Date: 1998
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0605-7_11

Ordering information: This item can be ordered from
http://www.springer.com/9781461206057

DOI: 10.1007/978-1-4612-0605-7_11

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().