فضای تایشمولر
در ریاضیات، فضای تایشمولر (به انگلیسی: Teichmüller Space)، از یک رویه توپولوژیکی (یا دیفرانسیل) (حقیقی) چون
هر نقطه از فضای تایشمولر
فضای تایشمولر دارای ساختار منیفلد مختلط کانونی بوده و متریک طبیعی غنی ای دارد. مطالعه ویژگی هندسی چنین ساختارهای متنوع، حوزه تحقیقاتی فعالی است.
منابع
- Ahlfors, Lars V. (2006). Lectures on quasiconformal mappings. Second edition. With supplemental chapters by C. J. Earle, I. Kra, M. Shishikura and J. H. Hubbard. American Math. Soc. pp. viii+162. ISBN 978-0-8218-3644-6.
- Bers, Lipman (1970), "On boundaries of Teichmüller spaces and on Kleinian groups. I", Annals of Mathematics, Second Series, 91 (3): 570–600, doi:10.2307/1970638, JSTOR 1970638, MR 0297992
- Fathi, Albert; Laudenbach, François; Poenaru, Valentin (2012). Thurston's work on surfaces. Princeton University Press. pp. xvi+254. ISBN 978-0-691-14735-2. MR 3053012.
- Gardiner, Frederic P.; Masur, Howard (1991), "Extremal length geometry of Teichmüller space", Complex Variables Theory Appl., 16 (2–3): 209–237, doi:10.1080/17476939108814480, MR 1099913
- Imayoshi, Yôichi; Taniguchi, Masahiko (1992). An introduction to Teichmüller spaces. Springer. pp. xiv+279. ISBN 978-4-431-70088-3.
- Kerckhoff, Steven P. (1983). "The Nielsen realization problem". Annals of Mathematics. Second Series. 117 (2): 235–265. CiteSeerX 10.1.1.353.3593. doi:10.2307/2007076. JSTOR 2007076. MR 0690845.
- McMullen, Curtis T. (2000), "The moduli space of Riemann surfaces is Kähler hyperbolic", Annals of Mathematics, Second Series, 151 (1): 327–357, arXiv:math/0010022, doi:10.2307/121120, JSTOR 121120, MR 1745010
- Ratcliffe, John (2006). Foundations of hyperbolic manifolds, Second edition. Springer. pp. xii+779. ISBN 978-0387-33197-3.
- Thurston, William P. (1988), "On the geometry and dynamics of diffeomorphisms of surfaces", Bulletin of the American Mathematical Society, New Series, 19 (2): 417–431, doi:10.1090/S0273-0979-1988-15685-6, MR 0956596
مطالعه بیشتر
- Bers, Lipman (1981), "Finite-dimensional Teichmüller spaces and generalizations", Bulletin of the American Mathematical Society, New Series, 5 (2): 131–172, doi:10.1090/S0273-0979-1981-14933-8, MR 0621883
- Gardiner, Frederick P. (1987), Teichmüller theory and quadratic differentials, Pure and Applied Mathematics (New York), New York: John Wiley & Sons, ISBN 978-0-471-84539-3, MR 0903027
- Hubbard, John Hamal (2006), Teichmüller theory and applications to geometry, topology, and dynamics. Vol. 1, Matrix Editions, Ithaca, NY, ISBN 978-0-9715766-2-9, MR 2245223
- Papadopoulos, Athanase, ed. (2007–2016), Handbook of Teichmüller theory. Vols. I-V, IRMA Lectures in Mathematics and Theoretical Physics, vol. 11, 13, 17, 19, 26, European Mathematical Society (EMS), Zürich, doi:10.4171/029, ISBN 978-3-03719-029-6, MR 2284826 The last volume contains translations of several of Teichmüller's papers.
- Teichmüller, Oswald (1939), "Extremale quasikonforme Abbildungen und quadratische Differentiale", Abh. Preuss. Akad. Wiss. Math.-Nat. Kl., 1939 (22): 197, JFM 66.1252.01, MR 0003242
- Teichmüller, Oswald (1982), Ahlfors, Lars V.; Gehring, Frederick W. (eds.), Gesammelte Abhandlungen, Berlin, New York: Springer-Verlag, ISBN 978-3-540-10899-3, MR 0649778
- Voitsekhovskii, M.I. (2001) [1994], "فضای تایشمولر", Encyclopedia of Mathematics, EMS Press