On a theorem of Lindelöf
Vladimir Gutlyanskii; Olli Martio; Vladimir Ryazanov
Annales UMCS, Mathematica (2011)
- Volume: 65, Issue: 2, page 45-51
- ISSN: 2083-7402
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topVladimir Gutlyanskii, Olli Martio, and Vladimir Ryazanov. "On a theorem of Lindelöf." Annales UMCS, Mathematica 65.2 (2011): 45-51. <http://eudml.org/doc/267886>.
@article{VladimirGutlyanskii2011,
abstract = {We give a quasiconformal version of the proof for the classical Lindelöf theorem: Let f map the unit disk D conformally onto the inner domain of a Jordan curve C. Then C is smooth if and only if arh f'(z) has a continuous extension to D. Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.},
author = {Vladimir Gutlyanskii, Olli Martio, Vladimir Ryazanov},
journal = {Annales UMCS, Mathematica},
keywords = {Lindelöf theorem; infinitesimal geometry; continuous extension to the boundary; differentiability at the boundary; conformal and quaisconformal mappings; conformal mappings; quasiconformal mappings; boundary extension},
language = {eng},
number = {2},
pages = {45-51},
title = {On a theorem of Lindelöf},
url = {http://eudml.org/doc/267886},
volume = {65},
year = {2011},
}
TY - JOUR
AU - Vladimir Gutlyanskii
AU - Olli Martio
AU - Vladimir Ryazanov
TI - On a theorem of Lindelöf
JO - Annales UMCS, Mathematica
PY - 2011
VL - 65
IS - 2
SP - 45
EP - 51
AB - We give a quasiconformal version of the proof for the classical Lindelöf theorem: Let f map the unit disk D conformally onto the inner domain of a Jordan curve C. Then C is smooth if and only if arh f'(z) has a continuous extension to D. Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.
LA - eng
KW - Lindelöf theorem; infinitesimal geometry; continuous extension to the boundary; differentiability at the boundary; conformal and quaisconformal mappings; conformal mappings; quasiconformal mappings; boundary extension
UR - http://eudml.org/doc/267886
ER -
References
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- Gutlyanskii, V. Ya., Martio, O., Ryazanov, V. I. and Vuorinen, M., Infinitesimal geometry of quasiregular mappings, Ann. Acad. Sci. Fenn. Math. 25 (2000), no. 1, 101-130. Zbl0938.30014
- Lehto, O., Virtanen, K. I., Quasiconformal Mappings in the Plane, 2nd Edition, Springer-Verlag, Berlin-Heidelberg-New York, 1973. Zbl0267.30016
- Lindelöf, E., Sur la représentation conforme d'une aire simplement connexe sur l'aire d'un cercle, Quatriéme Congrés des Mathématiciens Scandinaves, Stockholm, 1916, pp. 59-90. Zbl47.0322.04
- Pommerenke, Ch., Boundary Behaviour of Conformal Maps, Springer-Verlag, Berlin-Heidelberg-New York, 1992. Zbl0762.30001
- Warschawski, S. E., On differentiability at the boundary in conformal mapping, Proc. Amer. Math. Soc. 12 (1961), 614-620. Zbl0100.28803
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