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Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards. (English) Zbl 0676.32006
Invent. Math. 97, No. 3, 553-583 (1989); erratum ibid. 103, No. 2, 447 (1991).
This paper is concerned with some special aspects of Teichmüller theory and applications to billiards. From the summary: “There exists a Teichmüller disc \(\Delta_ n\) containing the Riemann surface of \(y^ 2+x^ n=1,\) in the genus [(n-1)/2] Teichmüller space, such that the stabilizer of \(\Delta_ n\) in the mapping class group has a fundamental domain of finite (Poincaré) volume in \(\Delta_ n\). Application is given to an asymptotic formula for the length spectrum of the billiard in isosceles triangles with angles (\(\pi\) /n,\(\pi\) /n,((n-2)/n)\(\pi)\) and to the uniform distribution of infinite billiard trajectories in the same triangles.”
Reviewer: S.Kosarew

MSC:
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
30F30 Differentials on Riemann surfaces
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