Geodesic
On the gradient of the conformal radius of a plane domain
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 1, pp. 167-178

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This paper studies the quasi-conformality of domain mapping by the gradient of the conformal radius. It is proved that the gradient of the conformal radius realizes quasi-conformal mapping for domains with convex boundaries. For these domains we obtain new estimates of the quasi-conformality coefficient of the conformal radius gradient.
Keywords: quasi-conformal mapping, conformal radius, gradient of the conformal radius
Mots-clés : convex domain. 
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     author = {L. A. Aksentyev and A. N. Akhmetova},
     title = {On the gradient of the conformal radius of a~plane domain},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {167--178},
     publisher = {mathdoc},
     volume = {154},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_1_a14/}
}
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L. A. Aksentyev; A. N. Akhmetova. On the gradient of the conformal radius of a plane domain. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 1, pp. 167-178. http://geodesic.mathdoc.fr/item/UZKU_2012_154_1_a14/