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Logarithmic law for geodesics in moduli space. (English) Zbl 0790.32022

Bödigheimer, Carl-Friedrich (ed.) et al., Mapping class groups and moduli spaces of Riemann surfaces. Proceedings of workshops held June 24-28, 1991, in Göttingen, Germany, and August 6-10, 1991, in Seattle, WA (USA). Providence, RI: American Mathematical Society. Contemp. Math. 150, 229-245 (1993).
The author studies one more analogy between hyperbolic and Teichmüller spaces. Namely he proves that a logarithmic law for geodesics in hyperbolic manifold established by D. Sullivan (1982) is valid also for geodesics on Teichmüller space. It means that the geodesic \(A_ t\) in the moduli space, determined by an almost every quadratic differential, satisfies the equality \[ \limsup_{t\to\infty}\tau(A_ t,A_ 0)/\log t=I/2 \] where \(\tau(A,B)\) is the Teichmüller metric.
For the entire collection see [Zbl 0777.00025].

MSC:

32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
32Q45 Hyperbolic and Kobayashi hyperbolic manifolds
30F60 Teichmüller theory for Riemann surfaces
30F30 Differentials on Riemann surfaces
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