Hausdorff dimension of divergent Teichmüller geodesics
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- by Howard Masur PDF
- Trans. Amer. Math. Soc. 324 (1991), 235-254 Request permission
Abstract:
Let $g > 1$ be given and let $k = ({k_1}, \ldots ,{k_n})$ be an $n$-tuple of positive integers whose sum is $4g - 4$. Denote by ${Q_k}$ the set of all holomorphic quadratic differentials on compact Riemann surfaces of genus $g$ whose zeros have orders ${k_1}, \ldots , {k_n}$. $Q_k$ is called a stratum inside the cotangent space of all holomorphic quadratic differentials over the Teichmüller space of genus $g$. Let ${Q_k}/\operatorname {Mod} (g)$ be the moduli space where $\operatorname {Mod} (g)$ is the mapping class group. Each $q \in {Q_k}$ defines a Teichmüller geodesic. Theorem. There exists $\delta > 0$ so that for almost all $q \in {Q_k}$, the set of $\theta$, such that the geodesic defined by ${e^{i\theta }}q$ eventually leaves every compact set in ${Q_k}/\operatorname {Mod} (g)$, has Hausdorff dimension $\theta$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- 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