Universal Teichmüller space

Short description: Concept in mathematical complex analysis

In mathematical complex analysis, universal Teichmüller space T(1) is a Teichmüller space containing the Teichmüller space T(G) of every Fuchsian group G. It was introduced by Bers (1965) as the set of boundary values of quasiconformal maps of the upper half-plane that fix 0, 1, and ∞.

References

• Bers, Lipman (1965), "Automorphic forms and general Teichmüller spaces", in Aeppli, A.; Calabi, Eugenio; Röhrl, H., Proceedings of the Conference on Complex Analysis, Minneapolis 1964, Berlin, New York: Springer-Verlag, pp. 109–113, ISBN 9783540033851, https://books.google.com/books?id=aCbvAAAAMAAJ 
• Bers, Lipman (1970), "Universal Teichmüller space", in Gilbert, Robert P.; Newton, Roger G., Analytic methods in mathematical physics (Sympos., Indiana Univ., Bloomington, Ind., 1968), Gordon and Breach, pp. 65–83, ISBN 9780677135601, https://books.google.com/books?id=hqTvAAAAMAAJ 
• Bers, Lipman (1972), "Uniformization, moduli, and Kleinian groups", The Bulletin of the London Mathematical Society 4 (3): 257–300, doi:10.1112/blms/4.3.257, ISSN 0024-6093 
• Gardiner, Frederick P.; Harvey, William J. (2002), "Universal Teichmüller space", Handbook of complex analysis: geometric function theory, Vol. 1, Handbook of Complex Analysis, 1, Amsterdam: North-Holland, pp. 457–492, doi:10.1016/S1874-5709(02)80016-6, ISBN 9780444828453 
• Pekonen, Osmo (1995), "Universal Teichmüller space in geometry and physics", Journal of Geometry and Physics 15 (3): 227–251, doi:10.1016/0393-0440(94)00007-Q, ISSN 0393-0440, Bibcode: 1995JGP....15..227P