# Short separating geodesics for multiply connected domains

Open Mathematics (2011)

- Volume: 9, Issue: 5, page 984-996
- ISSN: 2391-5455

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topMark Comerford. "Short separating geodesics for multiply connected domains." Open Mathematics 9.5 (2011): 984-996. <http://eudml.org/doc/269176>.

@article{MarkComerford2011,

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.},

author = {Mark Comerford},

journal = {Open Mathematics},

keywords = {Hyperbolic Geodesics; Meridians; hyperbolic geodesics; meridians; multiply connected domains},

language = {eng},

number = {5},

pages = {984-996},

title = {Short separating geodesics for multiply connected domains},

url = {http://eudml.org/doc/269176},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Mark Comerford

TI - Short separating geodesics for multiply connected domains

JO - Open Mathematics

PY - 2011

VL - 9

IS - 5

SP - 984

EP - 996

AB - 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.

LA - eng

KW - Hyperbolic Geodesics; Meridians; hyperbolic geodesics; meridians; multiply connected domains

UR - http://eudml.org/doc/269176

ER -

## References

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