S. L. Krushkal', “Complex geometry of the universal Teichmüller space”, Sibirsk. Mat. Zh., 45:4 (2004), 780–808; Siberian Math. J., 45:4 (2004), 646

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Sibirskii Matematicheskii Zhurnal, 2004, Volume 45, Number 4, Pages 780–808 (Mi smj1106)

This article is cited in 10 scientific papers (total in 10 papers)

Complex geometry of the universal Teichmüller space

S. L. Krushkal'^ab

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Bar-Ilan University

Full-text PDF (385 kB) Citations (10)

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Abstract: We prove that all invariant distances on the universal Teichmüller space agree and are determined by the Grunsky coefficients of the naturally related conformal maps. This fact yields various important consequences; in particular, we obtain solutions of certain well-known geometric problems in complex analysis and related fields.

Keywords: Teichmüller space, Teichmüller metric, invariant distances, Kobayashi metric, Carathéodory metric, Grunsky coefficients, Green's function, plurisubharmonic function.

Received: 30.09.2003

English version:
Siberian Mathematical Journal, 2004, Volume 45, Issue 4, Pages 646–668
DOI: https://doi.org/10.1023/B:SIMJ.0000035830.46662.75

Bibliographic databases:

UDC: 517.54, 517.55

Language: Russian

Citation: S. L. Krushkal', “Complex geometry of the universal Teichmüller space”, Sibirsk. Mat. Zh., 45:4 (2004), 780–808; Siberian Math. J., 45:4 (2004), 646–668

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/smj1106

https://www.mathnet.ru/eng/smj/v45/i4/p780

This publication is cited in the following 10 articles:

Kuehnau R., “Quasiconformal Mappings With Replaced Dilatation”, Complex Analysis and Dynamical Systems Vi, Pt 2: Complex Analysis, Quasiconformal Mappings, Complex Dynamics, Contemporary Mathematics, 667, eds. Agranovsky M., BenArtzi M., Galloway G., Karp L., Khavinson D., Reich S., Weinstein G., Zalcman L., Amer Mathematical Soc, 2016, 181–186
Krushkal S.L., “the Grunsky Function and Caratheodory Metric of Teichmüller Spaces”, Complex Var. Elliptic Equ., 61:6 (2016), 803–816
Krushkal S.L., “Milin'S Coefficients, Complex Geometry of Teichmuller Spaces and Variational Calculus For Univalent Functions”, Georgian Math. J., 21:3 (2014), 313–332
Krushkal S.L., “Complex Homotopy and Grunsky Operator”, Complex Var. Elliptic Equ., 59:1, SI (2014), 48–58
Samuel L. Krushkal, “Hyperbolic metrics on universal Teichmüller space and extremal problems”, J Math Sci, 182:1 (2012), 70
E. M. Chirka, “Prostranstva Teikhmyullera”, Lekts. kursy NOTs, 15, MIAN, M., 2010, 3–150
Samuel L. Krushkal, “The dilatation function of a holomorphic isotopy”, Funct. Approx. Comment. Math., 40:1 (2009)
Krushkal S., “Complex geometry of the universal Teichmüller space. II”, Georgian Mathematical Journal, 14:3 (2007), 483–498
Shen Yu.-l., “On grunsky operator”, Science in China Series A–Mathematics, 50:12 (2007), 1805–1817
Krushkal S, Kuhnau R, “Grunsky inequalities and quasiconformal extension”, Israel Journal of Mathematics, 152 (2006), 49–59

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

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References:	54

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