Difference between revisions of "Teichmüller space"
From Encyclopedia of Mathematics
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A metric space with as points abstract Riemann surfaces (that is, classes of conformallyequivalent Riemann surfaces of genus (cf. Riemann surfaces, conformal classes of) with singled out equivalent (with respect to the identity mapping) systems of generators of the fundamental group , and in which the distance between and is equal to , where the constant is the dilatation of the Teichmüller mapping (of the quasiconformal mapping giving the smallest maximum dilatation among all such mappings). Introduced by O. Teichmüller [1].
References
[1]  O. Teichmüller, "Extremale quasikonforme Abbildungen und quadratische Differentialen" Abhandl. Preuss. Akad. Wissenschaft. Math.Nat. Kl. , 22 (1939) pp. 3–197 
[2a]  L. Bers, "Quasiconformal mappings and Teichmüller's theorem" R. Nevanlinna (ed.) et al. (ed.) , Analytic functions , Princeton Univ. Press (1960) pp. 89–119 
[2b]  L.V. Ahlfors, "The complex analytic structure of the space of Riemann surfaces" R. Nevanlinna (ed.) et al. (ed.) , Analytic functions , Princeton Univ. Press (1960) pp. 45–66 
[2c]  L. Bers, "Spaces of Riemann surfaces" , Proc. Intern. Congress Mathematicians, Edinburgh 1958 , Cambridge Univ. Press (1959) pp. 349–361 
[2d]  L. Bers, "Simultaneous uniformization" Bull. Amer. Math. Soc. , 66 (1960) pp. 94–97 
[2e]  L. Bers, "Holomorphic differentials as functions of moduli" Bull. Amer. Math. Soc. , 67 (1961) pp. 206–210 
[2f]  L. Ahlfors, "On quasiconformal mappings" J. d'Anal. Math. , 3 (1954) pp. 1–58; 207–208 
[3]  S.L. Krushkal, "Quasiconformal mappings and Riemann surfaces" , Halsted (1979) (Translated from Russian) 
Comments
References
[a1]  F.P. Gardiner, "Teichmüller theory and quadratic differentials" , Wiley (1987) 
[a2]  O. Lehto, "Univalent functions and Teichmüller spaces" , Springer (1987) 
[a3]  S. Nag, "The complex analytic theory of Teichmüller spaces" , Wiley (1988) 
How to Cite This Entry:
Teichmüller space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Teichm%C3%BCller_space&oldid=15836
Teichmüller space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Teichm%C3%BCller_space&oldid=15836
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics  ISBN 1402006098. See original article