The length of closed geodesics on random Riemann Surfaces
| dc.creator | Makover, Eran | |
| dc.creator | McGowan, Jeffrey | |
| dc.date | 2005-04-08 | |
| dc.date.accessioned | 2026-07-07T05:18:55Z | |
| dc.date.available | 2026-07-07T05:18:55Z | |
| dc.description | Short geodesics are important in the study of the geometry and the spectra of Riemann surfaces. Bers' theorem gives a global bound on the length of the first $3g-3$ geodesics. We use the construction of Brooks and Makover of random Riemann surfaces to investigate the distribution of short ($< \log (g)$) geodesics on a random Riemann surfaces. We calculate the expected value of the shortest geodesic, and show that if one orders prime non-intersecting geodesics by length $γ_1\le γ_2\le ... \le γ_i ,...$, then for fixed $k$, if one allows the genus to go to infinity, the length of $γ_{k}$ is independent of the genus. | |
| dc.description | 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0504175 | |
| dc.identifier | http://arxiv.org/abs/math/0504175 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74836 | |
| dc.subject | Differential Geometry | |
| dc.subject | Metric Geometry | |
| dc.subject | 58J50 | |
| dc.title | The length of closed geodesics on random Riemann Surfaces | |
| dc.type | text |