Hausdorff dimension of divergent Teichmüller geodesics

Author:
Howard Masur

Journal:
Trans. Amer. Math. Soc. **324** (1991), 235-254

MSC:
Primary 30F30; Secondary 28A75, 32G15, 58F17

DOI:
https://doi.org/10.1090/S0002-9947-1991-0984857-0

MathSciNet review:
984857

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be given and let be an -tuple of positive integers whose sum is . Denote by the set of all holomorphic quadratic differentials on compact Riemann surfaces of genus whose zeros have orders . is called a stratum inside the cotangent space of all holomorphic quadratic differentials over the Teichmüller space of genus . Let be the moduli space where is the mapping class group. Each defines a Teichmüller geodesic.

**Theorem**. *There exists* *so that for almost all* , *the set of* , *such that the geodesic defined by* *eventually leaves every compact set in* , *has Hausdorff dimension* .

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DOI:
https://doi.org/10.1090/S0002-9947-1991-0984857-0

Article copyright:
© Copyright 1991
American Mathematical Society