On the Number and Location of Short Geodesics in Moduli Space
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چکیده
A closed Teichmüller geodesic in the moduli space Mg of Riemann surfaces of genus g is called L-short if it has length at most L/g. We show that for any L > 0 there exist R > ǫ > 0, independent of g, so that the L-short geodesics in Mg all lie in the intersection of the ǫ-thick part and the R-thin part. We also estimate the number of L-short geodesics in Mg, bounding this from above and below by polynomials in g whose degrees depend on L and tend to infinity as L does.
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تاریخ انتشار 2012