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Dal'nevost. Mat. Zh., 2018, Volume 18, Number 2, Pages 233–241 (Mi dvmg385)  

On the conformal metric of annulus in the n-dimensional Euclidean space

E. G. Prilepkinaab, A. S. Afanaseva-Grigorevab

a Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
b Far Eastern Federal University, Vladivostok

Abstract: It is shown by the methods of symmetrization that the geodesic with respect to the conformal metric of annulus in the Euclidean space is located into a two-dimensional sector. As a consequence, the geodesic is established in the case of points located on symmetric sphere of the annulus. Exact lower bounds are proved for the conformal metric of the annulus. A distortion theorem for quasi-regular mappings is given.

Key words: conformal module, modulii of curve families, quasiregular mappings, annulus, distortion theorem.

Funding Agency Grant Number
Russian Science Foundation 14-11-00022


Full text: PDF file (542 kB)
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Document Type: Article
UDC: 517.54
MSC: 31B99
Received: 29.07.2018

Citation: E. G. Prilepkina, A. S. Afanaseva-Grigoreva, “On the conformal metric of annulus in the n-dimensional Euclidean space”, Dal'nevost. Mat. Zh., 18:2 (2018), 233–241

Citation in format AMSBIB
\Bibitem{PriAfa18}
\by E.~G.~Prilepkina, A.~S.~Afanaseva-Grigoreva
\paper On the conformal metric of annulus in the n-dimensional Euclidean
space
\jour Dal'nevost. Mat. Zh.
\yr 2018
\vol 18
\issue 2
\pages 233--241
\mathnet{http://mi.mathnet.ru/dvmg385}


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