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Russian Mathematical Surveys, 2012, Volume 67, Issue 6, Pages 1091–1165
DOI: https://doi.org/10.1070/RM2012v067n06ABEH004819 (Mi rm9499) 		 
This article is cited in 10 scientific papers (total in 11 papers)

Holomorphic motions and uniformization of holomorphic families of Riemann surfaces

E. M. Chirka

Steklov Mathematical Institute of the Russian Academy of Sciences
English version PDF (1044 kB) Citations (11)
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DOI: https://doi.org/10.1070/RM2012v067n06ABEH004819
Abstract: Sufficient conditions for the simultaneous uniformization of holomorphic families of Riemann surfaces are investigated. The main method is based on a local construction of holomorphic and almost holomorphic motions with subsequent use of the machinery of Teichmüller spaces. Holomorphic motions are also applied to the closely related problem of extending a complex structure.
Bibliography: 62 titles.
Keywords: Riemann surfaces, Teichmüller spaces, uniformization, holomorphic motions, removable singularities.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00495
11-01-12033-офи-м
Received: 08.10.2012
Russian version:
Uspekhi Matematicheskikh Nauk, 2012, Volume 67, Issue 6(408), Pages 125–202
DOI: https://doi.org/10.4213/rm9499
Bibliographic databases:
Document Type: Article
UDC: 517.545+517.554
MSC: Primary 30Fxx, 32Q30, 32Q60; Secondary 30C35, 30C62, 32G15, 37F30
Language: English
Original paper language: Russian
Citation: E. M. Chirka, “Holomorphic motions and uniformization of holomorphic families of Riemann surfaces”, Uspekhi Mat. Nauk, 67:6(408) (2012), 125–202; Russian Math. Surveys, 67:6 (2012), 1091–1165
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/rm/v67/i6/p125
    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:70
    First page:38
     
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