Geodesic
Mappings connected with the gradient of conformal radius
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2009), pp. 60-64

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In this paper we prove the following conformality criterion for the gradient of conformal radius $\nabla R(D,z)$ of a convex domain $D$: the boundary $\partial D$ has to be a circumference. We calculate coefficients $K(r)$ for $K(r)$-quasiconformal mappings $\nabla R(D(r),z)$, $D(r)\subset D$, $0$, and complete the results obtained by F. G. Avkhadiev and K.-J. Wirths for the structure of boundary elements of quasiconformal mappings of a domain $D$.
Keywords: conformal radius, $K$-quasiconformal mapping, Beltrami equation.
Mots-clés : gradient of conformal radius 
@article{IVM_2009_6_a7,
     author = {L. A. Aksent'ev and A. N. Akhmetova},
     title = {Mappings connected with the gradient of conformal radius},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {60--64},
     publisher = {mathdoc},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_6_a7/}
}
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L. A. Aksent'ev; A. N. Akhmetova. Mappings connected with the gradient of conformal radius. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2009), pp. 60-64. http://geodesic.mathdoc.fr/item/IVM_2009_6_a7/