Far Eastern Mathematical Journal

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


Prilepkina E.G., Afanaseva-Grigoreva A.S.

2018, issue 2, Ñ. 233-241


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.

Keywords:
conformal module, modulii of curve families, quasiregular mappings, annulus, distortion theorem

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