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How close are cone singularities on a random flat surface?

Alexey Rukhovich
Dec 2022
摘要
We study the shortest geodesics on flat cone spheres, i.e. flat metrics onthe sphere with conical singularities. The length of the shortest geodesicbetween two singular points can be treated as a function on the moduli space offlat cone spheres with prescribed angle defects. We prove a recurrent relationon the distribution of this function with respect to Thurston's volume form onthe moduli space.
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