Mappings of finite distortion: formation of cusps.
Pekka Koskela; Juhani Takkinen
Publicacions Matemàtiques (2007)
- Volume: 51, Issue: 1, page 223-242
- ISSN: 0214-1493
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topKoskela, Pekka, and Takkinen, Juhani. "Mappings of finite distortion: formation of cusps.." Publicacions Matemàtiques 51.1 (2007): 223-242. <http://eudml.org/doc/41894>.
@article{Koskela2007,
abstract = {In this paper we consider the extensions of quasiconformal mappings f: B → Ωs to the whole plane, when the domain Ωs is a domain with a cusp of degree s > 0 and thus not an quasidisc. While these mappings do not have quasiconformal extensions, they may have extensions that are homeomorphic mappings of finite distortion with an exponentially integrable distortion, but in such a case ∫2B exp(λK(x)) dx = ∞ for all λ > 1/s. Conversely, for a given s > 0 such a mapping is constructed with ∫2B exp(λK(x)) dx < ∞ for all λ < 1/s.},
author = {Koskela, Pekka, Takkinen, Juhani},
journal = {Publicacions Matemàtiques},
keywords = {Funciones de variable compleja; Aplicaciones cuasiconformes; Teoría geométrica de funciones; cusp; quasiconformal mappings; quasidisc},
language = {eng},
number = {1},
pages = {223-242},
title = {Mappings of finite distortion: formation of cusps.},
url = {http://eudml.org/doc/41894},
volume = {51},
year = {2007},
}
TY - JOUR
AU - Koskela, Pekka
AU - Takkinen, Juhani
TI - Mappings of finite distortion: formation of cusps.
JO - Publicacions Matemàtiques
PY - 2007
VL - 51
IS - 1
SP - 223
EP - 242
AB - In this paper we consider the extensions of quasiconformal mappings f: B → Ωs to the whole plane, when the domain Ωs is a domain with a cusp of degree s > 0 and thus not an quasidisc. While these mappings do not have quasiconformal extensions, they may have extensions that are homeomorphic mappings of finite distortion with an exponentially integrable distortion, but in such a case ∫2B exp(λK(x)) dx = ∞ for all λ > 1/s. Conversely, for a given s > 0 such a mapping is constructed with ∫2B exp(λK(x)) dx < ∞ for all λ < 1/s.
LA - eng
KW - Funciones de variable compleja; Aplicaciones cuasiconformes; Teoría geométrica de funciones; cusp; quasiconformal mappings; quasidisc
UR - http://eudml.org/doc/41894
ER -
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