Geodesic-length functions and the Weil-Petersson curvature tensor
نویسندگان
چکیده
منابع مشابه
The Weil-petersson Geodesic Flow Is Ergodic
We prove that the geodesic flow for the Weil-Petersson metric on the moduli space of Riemann surfaces is ergodic (and in fact Bernoulli) and has finite, positive metric entropy.
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We present a brief but nearly self-contained proof of a formula for the Weil-Petersson Hessian of the geodesic length of a closed curve (either simple or not simple) on a hyperbolic surface. The formula is the sum of the integrals of two naturally defined positive functions over the geodesic, proving convexity of this functional over Teichmuller space (due to Wolpert (1987)). We then estimate t...
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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 the mapping class group. His proof inv...
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We formulate and describe a visual compactification of the Teichmüller space by Weil-Petersson geodesic rays emanating from a point X. We focus on analogies with Bers’s compactification: due to non-completeness, finite rays correspond to cusps, and such cusps are dense in the visual sphere. By analogy with a result of Kerckhoff and Thurston, we show the natural action of the mapping class group...
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Since notions of coarse geometry and quasi-isometries were first introduced by M. Gromov, many studies of geometry have been renovated with its rough perspective. In this note we give an expository account of results of [Br] and of joint work of the author with Benson Farb [BF] that apply such a coarse point of view to the Weil-Petersson metric on Teichmüller space. A natural graph of pants dec...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2012
ISSN: 0022-040X
DOI: 10.4310/jdg/1344430826