Howard A. Masur

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This paper concerns the interplay between the complex structure of a Riemann surface and the essentially Euclidean geometry induced by a quadratic differential. One aspect of this geometry is the " trajectory structure" of a quadratic differential which has long played a central role in Teichmfiller theory starting with Teichmiiller's proof of the existence(More)
A theory of random walks on the mapping class group and its non-elementary subgroups is developed. We prove convergence of sample paths in the Thurston compact-iication and show that the space of projective measured foliations with the corresponding harmonic measure can be identiied with the Poisson boundary of random walks. The methods are based on an(More)
To every compact orientable surface one can associate following Harvey Ha Ha a combinatorial object the so called complex of curves which is analogous to Tits buildings associated to semisimple Lie groups The basic result of the present paper is an analogue of a fundamental theorem of Tits for these complexes It asserts that every automorphism of the(More)
Let S be a surface of genus g with n punctures, and assume 3g − 3 + n > 1. Associated to S is an object C(S) called the complex of curves, whose vertices are homotopy classes of nontrivial, nonperipheral simple closed curves. A k-simplex of C(S) is a collection of k + 1 disjoint nonperipheral homotopically distinct simple closed curves. The dimension of the(More)
Let F = Fg,n be a surface of genus g with n punctures. We assume 3g − 3 + n > 1 and that (g, n) 6= (1, 2). The purpose of this paper is to prove, for the Weil-Petersson metric on Teichmuller space Tg,n, the analogue of Royden’s famous result [15] that every complex analytic isometry of Tg,0 with respect to the Teichmuller metric is induced by an element of(More)
1 Polygonal billiards, rational billiards 3 1.1 Polygonal billiards . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Examples: a pair of elastic point-masses on a segment and a triple of point-masses on a circle . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Unfolding billiard trajectories, rational polygons . . . . . . . . . . . . 5(More)
We analyze the coarse geometry of the Weil-Petersson metric on Teichmüller space, focusing on applications to its synthetic geometry (in particular the behavior of geodesics). We settle the question of the strong relative hyperbolicity of the Weil-Petersson metric via consideration of its coarse quasi-isometric model, the pants graph. We show that in(More)