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

E. G. Prilepkina^ab, A. S. Afanaseva-Grigoreva<sup>b

a</sup> 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.

UDC: 517.54

MSC: 31B99

Received: 29.07.2018