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Uspekhi Mat. Nauk, 2017, Volume 72, Issue 3(435), Pages 97–130 (Mi umn9771)  

This article is cited in 3 scientific papers (total in 3 papers)

Geometric estimates for the Schwarzian derivative

V. N. Dubininab

a Far Eastern Federal University
b Institute for Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences

Abstract: This paper is a survey of results involving the Schwarzian derivative and depending on the geometry of the image of a domain under a holomorphic map. The author's results obtained previously by using the theory of condenser capacity and symmetrization constitute the core of the paper. Inequalities for univalent and multivalent functions are considered both at interior and at boundary points of the domain of definition. Auxiliary results and proofs of some of the theorems are presented.
Bibliography: 52 titles.

Keywords: Schwarzian derivative, holomorphic functions, boundary distortion, condenser capacity, symmetrization.

Funding Agency Grant Number
Russian Science Foundation 14-11-00022
This research was financed by a grant of the Russian Science Foundation (project no. 14-11-00022).


DOI: https://doi.org/10.4213/rm9771

Full text: PDF file (739 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2017, 72:3, 479–511

Bibliographic databases:

UDC: 517.54
MSC: Primary 30C25, 30C80, 30C85; Secondary 30C55, 30C75
Received: 23.03.2017

Citation: V. N. Dubinin, “Geometric estimates for the Schwarzian derivative”, Uspekhi Mat. Nauk, 72:3(435) (2017), 97–130; Russian Math. Surveys, 72:3 (2017), 479–511

Citation in format AMSBIB
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  • https://doi.org/10.4213/rm9771
  • http://mi.mathnet.ru/eng/umn/v72/i3/p97

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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. V. N. Dubinin, “Two-point distortion theorems and the Schwarzian derivatives of meromorphic functions”, J. Math. Anal. Appl., 467:1 (2018), 371–378  crossref  mathscinet  zmath  isi  scopus
    2. S. I. Bezrodnykh, “The Lauricella hypergeometric function $F_D^{(N)}$, the Riemann–Hilbert problem, and some applications”, Russian Math. Surveys, 73:6 (2018), 941–1031  mathnet  crossref  crossref  adsnasa  isi  elib
    3. Bolotnikov V., “Several Inequalities For the Schwarzian Derivative of a Bounded Analytic Function”, Complex Var. Elliptic Equ., 64:7 (2019), 1093–1102  crossref  mathscinet  zmath  isi  scopus
  • Успехи математических наук Russian Mathematical Surveys
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