About distortion theorems for one class quasi-conformal mappings, conformal outside a ring
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2009), pp. 65-74
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The author considers the class of quasiconformal homeomorphisms of extended complex plane onto itself, such as $f(\infty)=\infty$, $f'(\infty)=1$, $f(0)=0$. The area theorem was derived in the form of inequality for Grunsky coefficients. This inequality can be used for estimate functionals such as distortion theorems. Sufficient conditions of univalence functions $f(z)$ of this class are given.
Keywords:
quasi-conformal homeomorphism, Grunsky coefficients, conditions of univalence,
area theorems.
@article{VTGU_2009_4_a5,
author = {V. A. Shchepetev},
title = {About distortion theorems for one class quasi-conformal mappings, conformal outside a ring},
journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
pages = {65--74},
publisher = {mathdoc},
number = {4},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTGU_2009_4_a5/}
}
TY - JOUR AU - V. A. Shchepetev TI - About distortion theorems for one class quasi-conformal mappings, conformal outside a ring JO - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika PY - 2009 SP - 65 EP - 74 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VTGU_2009_4_a5/ LA - ru ID - VTGU_2009_4_a5 ER -
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V. A. Shchepetev. About distortion theorems for one class quasi-conformal mappings, conformal outside a ring. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2009), pp. 65-74. http://geodesic.mathdoc.fr/item/VTGU_2009_4_a5/