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Lines of minima and Teichmuller geodesics
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Choi, Young-Eun, Rafi, Kasra and Series, Caroline (2008) Lines of minima and Teichmuller geodesics. Geometric and Functional Analysis, Vol.18 (No.3). pp. 698-754. doi:10.1007/s00039-008-0675-6 ISSN 1016-443X.
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Official URL: http://dx.doi.org/10.1007/s00039-008-0675-6
Abstract
For two measured laminations nu(+) and nu(-) that fill up a hyperbolizable surface S and for t epsilon (-infinity, infinity), let L-t be the unique hyperbolic surface that minimizes the length function e(t)l(nu(+)) + e(-t)l(nu(-)) on Teichmuller space. We characterize the curves that are short in Lt and estimate their lengths. We find that the short curves coincide with the curves that are short in the surface g(t) on the Teichmuller geodesic whose horizontal and vertical foliations are respectively, e(t)nu(+) and e(-t)nu(-). By deriving additional information about the twists of nu(+) and nu(-) around the short curves, we estimate the Teichmuller distance between L-t and g(t). We deduce that this distance can be arbitrarily large, but that if S is a once-punctured torus or four-times-punctured sphere, the distance is bounded independently of t.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Teichmüller spaces, Geodesics (Mathematics), Maxima and minima, Geometry, Hyperbolic | ||||
| Journal or Publication Title: | Geometric and Functional Analysis | ||||
| Publisher: | Birkhaeuser Verlag AG | ||||
| ISSN: | 1016-443X | ||||
| Official Date: | September 2008 | ||||
| Dates: |
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| Volume: | Vol.18 | ||||
| Number: | No.3 | ||||
| Number of Pages: | 57 | ||||
| Page Range: | pp. 698-754 | ||||
| DOI: | 10.1007/s00039-008-0675-6 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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