Lines of minima and Teichmuller geodesics
| dc.creator | Choi, Young-Eun | |
| dc.creator | Rafi, Kasra | |
| dc.creator | Series, Caroline | |
| dc.date | 2006-05-04 | |
| dc.date | 2007-06-14 | |
| dc.date.accessioned | 2026-07-07T08:09:56Z | |
| dc.date.available | 2026-07-07T08:09:56Z | |
| dc.description | For two measured laminations $ν^+$ and $ν^-$ that fill up a hyperbolizable surface $S$ and for $t \in (-\infty, \infty)$, let $L_t$ be the unique hyperbolic surface that minimizes the length function $e^t l(ν^+) + e^{-t} l(ν^-)$ on Teichmuller space. We characterize the curves that are short in $L_t$ 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, $e^t ν^+$ and $e^{-t} ν^-$. By deriving additional information about the twists of $ν^+$ and $ν^-$ 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 $t$. | |
| dc.description | 58 pages, includes appendix and 9 figures; v2: corrections and revised exposition; to appear in Geometric and Functional Analysis | |
| dc.identifier | https://arxiv.org/abs/math/0605135 | |
| dc.identifier | http://arxiv.org/abs/math/0605135 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131694 | |
| dc.subject | Geometric Topology | |
| dc.subject | 30F60 | |
| dc.title | Lines of minima and Teichmuller geodesics | |
| dc.type | text |