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Russian Mathematical Surveys, 2017, Volume 72, Issue 3, Pages 479–511
DOI: https://doi.org/10.1070/RM9771 (Mi rm9771) 		 
This article is cited in 8 scientific papers (total in 8 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
English version PDF (692 kB) Citations (8)
References:
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DOI: https://doi.org/10.1070/RM9771
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).
Received: 23.03.2017
Russian version:
Uspekhi Matematicheskikh Nauk, 2017, Volume 72, Issue 3(435), Pages 97–130
DOI: https://doi.org/10.4213/rm9771
Bibliographic databases:
Document Type: Article
UDC: 517.54
MSC: Primary 30C25, 30C80, 30C85; Secondary 30C55, 30C75
Language: English
Original paper language: Russian
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://www.mathnet.ru/eng/rm/v72/i3/p97
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:784
    Russian version PDF:142
    English version PDF:54
    References:81
    First page:58
     
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