Geodesic
On the conformal metric of annulus in the n-dimensional Euclidean
Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 2, pp. 233-241 
E. G. Prilepkina; A. S. Afanaseva-Grigoreva. On the conformal metric of annulus in the n-dimensional Euclidean. Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 2, pp. 233-241. http://geodesic.mathdoc.fr/item/DVMG_2018_18_2_a11/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] M. Vuorinen, “Conformal geometry and quasiregular mappings”, Lecture Notes in Mathematics, Springer-Verlag, 1988 | DOI | MR

[2] I. S. Gal, “Conformally invariant metrics and uniform structures”, Indag. Math., 22 (1960), 218–244 | DOI | MR

[3] V. N. Dubinin, Emkosti kondensatorov i simmetrizatsiya v geometricheskoi teorii funktsii kompleksnogo peremennogo, Dalnauka, Vladivostok, 2009

[4] A. Yu. Solynin, “Continuous symmetrization via polarization”, Algebra i analiz, 24:1 (2012), 157–222 | MR

[5] J. Sarvas, “Symmetrization of condensers in n - space”, Ann. Acad. Sci. Fenn, Ser AI, 522 (1972), 1–44 | MR

[6] E. G. Akhmedzyanova, “Simmetrizatsiya otnositelno gipersfery”, Dalnevost. matem. sb., 1995, no. 1, 40–50 | Zbl

[7] V. N. Dubinin, “Preobrazovanie kondensatorov v prostranstve”, Dokl. AN SSSR, 296 (1987), 18–20

[8] E. V. Kostyuchenko, E. G. Prilepkina, “O polyarizatsii otnositelno gipersfery”, Dalnevost. matem. zhurn., 5:1 (2004), 22–29 | MR

[9] A. V. Sychev, Moduli i prostranstvennye kvazikonformnye otobrazheniya, Nauka, Moskva, 1983

[10] B. E. Levitskii, “K-simmetrizatsiya i ekstremalnye koltsa”, V sb. “Matematicheskii analiz”, 1971, 35–40 | MR

[11] M. A. Lavrentev, B. V. Shabat, Metody teorii funktsii kompleksnogo peremennogo, Nauka, Moskva, 1973