Asymptotical behavior of the conformal modulus of doubly connected planar domain under unbounded stretching along the abscissa axis

1 Jul 2021, 16:30


Semen Nasyrov (Kazan Federal University)


Conformal moduli of doubly connected domains and quadrilaterals play an important role in investigation of various problems of the theory of conformal and quasiconformal mappings. One of the simplest quasiconformal mappings is the stretching along the abscissa axis. In 2005 Prof. Vourinen suggested the problem of finding the asymptotics of the conformal modulus of a doubly connected planar domain under stretching it along the abscissa axis, as the coefficient of stretching tends to infinity. We discuss the problem in the cases of bounded and unbounded domains and, for some types of domains, find the main term of the asymptotics. Our study is based on the methods of geometric functions of a complex variable, in particular, on some results by Ahlfors and Warshavskii.

Primary author

Semen Nasyrov (Kazan Federal University)


Dina Dautova Van Giang Nguyen

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