Geodesic
On Mappings Related to the Gradient of the Conformal Radius
Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 3-12

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We establish a criterion for the gradient $\nabla R(D,z)$ of the conformal radius of a convex domain $D$ to be conformal: the boundary $\partial D$ must be a circle. We obtain estimates for the coefficients $K(r)$ for the $K(r)$-quasiconformal mappings $\nabla R(D,z)$, $D(r)\subset D$, $0$, and supplement the results of Avkhadiev and Wirths concerning the structure of the boundary under diffeomorphic mappings of the domain $D$.
Keywords: conformal radius, gradient of the conformal radius, convex mapping
Mots-clés : coefficient of quasiconformality, astroid, cycloid, hypocycloid. 
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     author = {L. A. Aksent'ev and A. N. Akhmetova},
     title = {On {Mappings} {Related} to the {Gradient} of the {Conformal} {Radius}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {3--12},
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     volume = {87},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a0/}
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L. A. Aksent'ev; A. N. Akhmetova. On Mappings Related to the Gradient of the Conformal Radius. Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a0/