Kleinian groups and the complex of curves.
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We consider the following questions: given a hyperbolic plane domain and a separation of its complement into two disjoint closed sets each of which contains at least two points, what is the shortest closed hyperbolic geodesic which separates these sets and is it a simple closed curve? We show that a shortest geodesic always exists although in general it may not be simple. However, one can also always find a shortest simple curve and we call such a geodesic a meridian of the domain. We...