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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2013, Volume 155, Book 2, Pages 65–82 (Mi uzku1198)  

This article is cited in 6 scientific papers (total in 6 papers)

Gakhov Set in the Hornich Space under the Bloch Restriction on Pre-Schwarzians

A. V. Kazantsev

Kazan (Volga Region) Federal University

Abstract: Gakhov set contains exactly those functions in the Hornich space over the unit disk which have the unique critical point of the conformal radius. The position of the intersection $\mathcal{A}$ of the Gakhov set and the Bloch space $\mathcal{B}$ is studied relative to the Banach structure of $\mathcal{B}$. A connection is revealed between the topological characteristics of the set $\mathcal{A}$ and the values of the curvature and index of the critical points for the functions in $\mathcal{A}$. An effective description is given for the set of points on the boundary of $\mathcal{A}$ with minimal pre-norm. By using the Minkowski functional, the starlikeness of the subset of the functions in $\mathcal{A}$ with the zero critical point of the conformal radius is established.

Keywords: hyperbolic derivative, conformal (inner mapping) radius, bifurcations of critical points, Hornich space, Bloch space, pre-Schwarzian, Gakhov set, interior and boundary of a set.

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UDC: 517.54+517.982.274
Received: 06.06.2012

Citation: A. V. Kazantsev, “Gakhov Set in the Hornich Space under the Bloch Restriction on Pre-Schwarzians”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 155, no. 2, Kazan University, Kazan, 2013, 65–82

Citation in format AMSBIB
\Bibitem{Kaz13}
\by A.~V.~Kazantsev
\paper Gakhov Set in the Hornich Space under the Bloch Restriction on Pre-Schwarzians
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2013
\vol 155
\issue 2
\pages 65--82
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1198}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Kazantsev, “O vykhode iz mnozhestva Gakhova, kontroliruemom usloviyami podchinennosti”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 156, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2014, 31–43  mathnet
    2. A. V. Kazantsev, “Ob uravnenii Gakhova v klassakh Yanovskogo s dopolnitelnym parametrom”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2015, 35–43  mathnet  elib
    3. A. V. Kazantsev, “O semeistvakh giperbolicheskikh proizvodnykh s kvazilevnerovskoi dinamikoi predshvartsianov”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 158, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2016, 66–80  mathnet  elib
    4. D. Kh. Giniyatova, “Otsenki gradienta giperbolicheskogo radiusa i neravenstva tipa Shvartsa–Pika dlya ekstsentricheskogo koltsa”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 158, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2016, 172–179  mathnet  elib
    5. A. V. Kazantsev, “Width of the Gakhov class over the Dirichlet space is equal to 2”, Lobachevskii J. Math., 37:4, SI (2016), 449–454  crossref  mathscinet  zmath  isi  elib
    6. A. M. Elizarov, A. V. Kazantsev, M. I. Kinder, “Strict superharmonicity of Mityuk's function for countably connected domains of simple structure”, Lobachevskii J. Math., 38:3, SI (2017), 408–413  crossref  mathscinet  zmath  isi  scopus
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