The Schwarzian derivative and measured laminations on Riemann surfaces
| dc.creator | Dumas, David | |
| dc.date | 2005-10-18 | |
| dc.date | 2006-12-20 | |
| dc.date.accessioned | 2026-07-07T07:36:18Z | |
| dc.date.available | 2026-07-07T07:36:18Z | |
| dc.description | We compare two relationships between quadratic differentials and measured geodesic laminations on hyperbolic Riemann surfaces (by foliations or complex projective structures). Each yields a homeomorphism $\ML(S) \to Q(X)$ for any conformal structure $X$ on a compact surface $S$. The main result is that these maps are nearly the same, differing by a multiplicative factor of -2 and an error term of lower order than the maps themselves (which we bound explicitly). As an application we show that the Schwarzian derivative of a $\CP^1$ structure with Fuchsian holonomy is close to a $2π$-integral Jenkins-Strebel differential. We also study compactifications of the space of $\CP^1$ structures using the Schwarzian derivative and grafting coordinates; we show that the natural map between these extends to the boundary of each fiber over Teichmuller space, and we describe this extension. | |
| dc.description | 36 pages, 5 figures; v3: important changes to account for correction to math.DG/0501194, also simplified some arguments | |
| dc.identifier | https://arxiv.org/abs/math/0510365 | |
| dc.identifier | http://arxiv.org/abs/math/0510365 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120381 | |
| dc.subject | Differential Geometry | |
| dc.subject | 30F60 (Primary) 30F45, 53C21, 57M50 (Secondary) | |
| dc.title | The Schwarzian derivative and measured laminations on Riemann surfaces | |
| dc.type | text |