Complex rigidity of Teichmu"ller spaces
Автор: Krushkal Samuel L.
Журнал: Математическая физика и компьютерное моделирование @mpcm-jvolsu
Рубрика: Математика труды III международной конференции "Геометрический анализ и его приложения"
Статья в выпуске: 6 (37), 2016 года.
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We outline old and new results concerning the well-known problems in the Teichmu¨ ller space theory, i.e., whether these spaces are starlike in the Bers holomorphic embedding and whether any Teichmu¨ ller space of dimension greater than 1 is biholomorhically equivalent to bounded convex domain in a complex Banach space.
Teichmu¨ ller spaces, holomorphic embeddings, schwarzian derivative, convex domain, starlike, holomorphic section, conformally rigid do- main, uniformly convex banach space
Короткий адрес: https://sciup.org/14968864
IDR: 14968864 | DOI: 10.15688/jvolsu1.2016.6.10
Список литературы Complex rigidity of Teichmu"ller spaces
- Abikoff W. A geometric property of Bers’ embedding of the Teichm¨ uller space. Riemann Surfaces and Related Topics (AM-97): Proceedings of the 1978 Stony Brook Conference (Ann. of Math. Stud.). Princeton, N. J., Princeton University Press, 1981, pp. 3-5.
- Astala K. Selfsimilar zippers. Holomorphic Functions and Moduli. New York, Springer, 1988, vol. I, pp. 61-73.
- Bers L., Kra I. A Crash Course on Kleinian Groups. Lecture Notes in Mathematics. Berlin, Springer, 1974, vol. 400, pp. 1-134.
- Bers L. On a theorem of Abikoff. Ann. Acad. Sci. Fenn. Ser. A. I. Math., 1985, vol. 10, pp. 83-87.
- Clunie J.G., Hallenbeck D.J., MacGregor T.H. A peaking and interpolation problem for univalent functions. J. Math. Anal. Appl., 1985, vol. 111, pp. 559-570.
- Earle C.J., Kra I. On sections of some holomorphic families of closed Riemann surfaces. Acta Math., 1976, vol. 137, pp. 49-79.
- Krushkal S.L. On shape of Hilbertian embedding of universal Teichmu¨ ller space. Transactions of Inst. of Math. Nat. Acad. Sciences of Ukraine (Zb. Pr. Inst. Mat. NAN Ukraine), 2015, vol. 12, no. 3, pp. 160-163.
- Krushkal S.L. On shape of Teichmu¨ ller spaces. Journal of Analysis, 2014, vol. 22, pp. 69-76.
- Krushkal S.L. On the question of the structure of the universal Teichmu¨ ller space. Soviet Math. Dokl., 1989, vol. 38, pp. 435-437.
- Krushkal S.L. Quasiconformal Mappings and Riemann Surfaces. New York, Wiley, 1979. 332 p.
- Krushkal S.L. Schwarzian derivative and complex Finsler metrics. Contemporary Mathematics, 2005, vol. 382, pp. 243-262.
- Krushkal S.L. Teichmu¨ ller spaces are not starlike. Ann. Acad. Sci. Fenn. Ser. A. I. Math., 1995, vol. 20, pp. 167-173.
- Lehto O. Univalent Functions and Teichmu¨ ller Spaces. New York, SpringerKVerlag, 1987. 260 p.
- Nag S. The Complex Analytic Theory of Teichmu¨ ller Spaces. New York, Wiley, 1988. 427 p.
- Thurston W.P. Zippers and univalent functions. The Bieberbach Conjecture: Proceedings of the Symposium on the Occasion of its Proof. Providence, R. I., Amer. Math. Soc., 1986, pp. 185K197.
- Toki M. On nonKstarlikeness of Teichmu¨ ller spaces. Proc. Japan Acad. Ser. A, 1993, vol. 69, pp. 58-60.
- Tukia P. The space of quasisymmetric mappings. Math. Scand., 1977, vol. 40, pp. 127-142.
- Zhuravlev I.V. A topological property of Teichmu¨ ller space. Math. Notes, 1985, vol. 38, pp. 803-804.