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2011 | 9 | 5 | 984-996
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Short separating geodesics for multiply connected domains

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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 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.
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  • University of Rhode Island
  • [1] Ahlfors L.V., Complex Analysis, 3rd ed., Internat. Ser. Pure Appl. Math., McGraw-Hill, New York, 1978
  • [2] Buser P., Geometry and Spectra of Compact Riemann Surfaces, Progr. Math., 106, Birkhäuser, Boston, 1992
  • [3] Buser P., Seppälä M., Short homology bases for Riemann surfaces, preprint available at
  • [4] Carleson L., Gamelin T.W., Complex Dynamics, Universitext Tracts Math., Springer, New York, 1993
  • [5] Comerford M., A straightening theorem for non-autonomous iteration, preprint available at
  • [6] Conway J.B., Functions of One Complex Variable, Grad. Texts in Math., 11, Springer, New York-Heidelberg, 1973
  • [7] Hubbard J.H., Teichmüller Theory and Applications to Geometry, Topology, and Dynamics - Volume 1: Teichmüller Theory, Matrix Editions, Ithaca, 2006
  • [8] Keen L., Lakic N., Hyperbolic Geometry from a Local Viewpoint, London Math. Soc. Stud. Texts, 68, Cambridge University Press, Cambridge, 2007
  • [9] Milnor J., Dynamics in One Complex Variable, 3rd ed., Ann. of Math. Stud., 160, Princeton University Press, Princeton, 2006
  • [10] Newman M.H.A., Elements of the Topology of Plane Sets of Points, 2nd ed., Cambridge University Press, Cambridge, 1961
  • [11] Parlier H., The homology systole of hyperbolic Riemann surfaces, Geom. Dedicata (in press), DOI: 10.1007/s10711-011-9613-0
  • [12] Parlier H., Separating simple closed geodesics and short homology bases on Riemann surfaces, preprint available at
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