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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, Number 6, Pages 60–64 (Mi ivm1464)  
This article is cited in 4 scientific papers (total in 4 papers)

Brief communications

Mappings connected with the gradient of conformal radius

L. A. Aksent'ev, A. N. Akhmetova

Chair of Mathematical Analysis, Kazan State University, Kazan, Russia
Full-text PDF (162 kB) Citations (4)
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Abstract: 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 $\nabla R(D(r),z)$, $D(r)\subset D$, $0<r<1$, and complete the results obtained by F. G. Avkhadiev and K.-J. Wirths for the structure of boundary elements of quasiconformal mappings of a domain $D$.
Keywords: conformal radius, gradient of conformal radius, $K$-quasiconformal mapping, Beltrami equation.
Received: 18.06.2007
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, Volume 53, Issue 6, Pages 49–52
DOI: https://doi.org/10.3103/S1066369X09060085
Bibliographic databases:
Document Type: Article
UDC: 517.546
Language: Russian
Citation: L. A. Aksent'ev, A. N. Akhmetova, “Mappings connected with the gradient of conformal radius”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 6, 60–64; Russian Math. (Iz. VUZ), 53:6 (2009), 49–52
Citation in format AMSBIB
\Bibitem{AksAkh09}
\by L.~A.~Aksent'ev, A.~N.~Akhmetova
\paper Mappings connected with the gradient of conformal radius
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2009
\issue 6
\pages 60--64
\mathnet{http://mi.mathnet.ru/ivm1464}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2584000}
\zmath{https://zbmath.org/?q=an:1177.30018}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2009
\vol 53
\issue 6
\pages 49--52
\crossref{https://doi.org/10.3103/S1066369X09060085}
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  • https://www.mathnet.ru/eng/ivm/y2009/i6/p60
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    This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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