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Uspekhi Mat. Nauk, 2012, Volume 67, Issue 6(408), Pages 125–202 (Mi umn9499)  

This article is cited in 4 scientific papers (total in 5 papers)

Holomorphic motions and uniformization of holomorphic families of Riemann surfaces

E. M. Chirka

Steklov Mathematical Institute of the Russian Academy of Sciences

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


DOI: https://doi.org/10.4213/rm9499

Full text: PDF file (1093 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2012, 67:6, 1091–1165

Bibliographic databases:

UDC: 517.545+517.554
MSC: Primary 30Fxx, 32Q30, 32Q60; Secondary 30C35, 30C62, 32G15, 37F30
Received: 08.10.2012

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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    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. T. Firsova, M. Lyubich, “$\lambda$-lemma for families of Riemann surfaces and the critical loci of complex Hénon maps”, Conform. Geom. Dyn., 21 (2017), 111–125  crossref  mathscinet  zmath  isi
    2. E. M. Chirka, “Orthogonal complex structures in $\mathbb{R}^4$”, Russian Math. Surveys, 73:1 (2018), 91–159  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. G. Gonzalez-Diez, S. Reyes-Carocca, “Families of Riemann surfaces, uniformization and arithmeticity”, Trans. Amer. Math. Soc., 370:3 (2018), 1529–1549  crossref  mathscinet  zmath  isi
    4. A. I. Aptekarev, V. K. Beloshapka, V. I. Buslaev, V. V. Goryainov, V. N. Dubinin, V. A. Zorich, N. G. Kruzhilin, S. Yu. Nemirovski, S. Yu. Orevkov, P. V. Paramonov, S. I. Pinchuk, A. S. Sadullaev, A. G. Sergeev, S. P. Suetin, A. B. Sukhov, K. Yu. Fedorovskiy, A. K. Tsikh, “Evgenii Mikhailovich Chirka (on his 75th birthday)”, Russian Math. Surveys, 73:6 (2018), 1137–1144  mathnet  crossref  crossref  adsnasa  isi  elib
    5. Gaussier H., Seshadri H., “Holomorphic Motions and Complex Geometry”, Proc. Amer. Math. Soc., 147:1 (2019), 301–313  crossref  mathscinet  zmath  isi  scopus
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