A ug 2 00 5 Immersions of Pants into a Fixed Hyperbolic Surface
نویسنده
چکیده
Exploiting a relationship between closed geodesics on a generic closed hyperbolic surface S and a certain unipotent flow on the product space T 1 (S) × T 1 (S), we obtain a local asymptotic equidistribution result for long closed geodesics on S. Applications include asymptotic estimates for the number of pants immersions into S satisfying various geometric constraints. Also we show that two closed geodesics γ 1 , γ 2 of length close to L chosen uniformly at random have a high probability of partially bounding an immersed 4-holed sphere whose other boundary components also have length close to L.
منابع مشابه
2 3 M ay 2 00 5 Immersions of Pants into a Fixed Hyperbolic Surface
Exploiting a relationship between closed geodesics on a generic closed hyperbolic surface S and a certain unipotent flow on the product space T 1 (S) × T 1 (S), we obtain a local asymptotic equidistribution result for long closed geodesics on S. Applications include asymptotic estimates for the number of pants immersions into S satisfying various geometric constraints. Also we show that two clo...
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