Difference between revisions of "Teichmüller space"
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A metric space with as points abstract Riemann surfaces (that is, classes of conformally-equivalent 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 quasi-conformal mapping giving the smallest maximum dilatation among all such mappings). Introduced by O. Teichmüller .
|||O. Teichmüller, "Extremale quasikonforme Abbildungen und quadratische Differentialen" Abhandl. Preuss. Akad. Wissenschaft. Math.-Nat. Kl. , 22 (1939) pp. 3–197|
|[2a]||L. Bers, "Quasi-conformal 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|
|||S.L. Krushkal, "Quasi-conformal mappings and Riemann surfaces" , Halsted (1979) (Translated from Russian)|
|[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)|
Teichmüller space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Teichm%C3%BCller_space&oldid=15836