Title

Short separating geodesics for multiply connected domains

Document Type

Article

Date of Original Version

10-1-2011

Abstract

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 prove that, although they are not in general uniquely defined, if one of the sets of the separation of the complement is connected, then they are unique and are also the shortest possible geodesics which separate the complement in this fashion. © Versita Warsaw and Springer-Verlag Wien.

Publication Title

Central European Journal of Mathematics

Volume

9

Issue

5

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