Short separating geodesics for multiply connected domains

• Autorzy: Mark Comerford
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Hyperbolic Geodesics; Meridians

Kategorie tematyczne

• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
• 30C20: Conformal mappings of special domains
• 30C75: Extremal problems for conformal and quasiconformal mappings, other methods

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 5
• Strony: 984-996

Daty

wydano

2011-10-01

online

2011-07-26

Twórcy

autor

Mark Comerford

• University of Rhode Island

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0065-4