Abstract
In this paper we prove the following conformity criterion for the gradient of conformal radius ∇R(D, z) of a convex domain D: the boundary ∂D has to be a circumference. We calculate coefficients K(r) for K(r)-quasiconformal mappings ∇R(D(r), z), D(r) ⊂ D, 0 < r < 1, and complete the results obtained by F. G. Avkhadiev and K.-J. Wirths for the structure of boundary elements of quasiconformal mappings of the domain D.
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References
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Original Russian Text © L.A. Aksent’ev and A.N. Akhmetova, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 6, pp. 60–64.
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Aksent’ev, L.A., Akhmetova, A.N. Mappings connected with the gradient of conformal radius. Russ Math. 53, 49–52 (2009). https://doi.org/10.3103/S1066369X09060085
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DOI: https://doi.org/10.3103/S1066369X09060085