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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
##### Keywords:
billiard theory; Teichmüller theory
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##### References:
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