A negative answer to Nevanlinna's type question and a parabolic surface with a lot of negative curvature
| dc.creator | Benjamini, Itai | |
| dc.creator | Merenkov, Sergei | |
| dc.creator | Schramm, Oded | |
| dc.date | 2002-09-25 | |
| dc.date | 2002-10-06 | |
| dc.date.accessioned | 2026-07-07T04:51:13Z | |
| dc.date.available | 2026-07-07T04:51:13Z | |
| dc.description | Consider a simply connected Riemann surface represented by a Speiser graph. Nevanlinna asked if the type of the surface is determined by the mean excess of the graph: whether mean excess zero implies that the surface is parabolic and negative mean excess implies that the surface is hyperbolic. Teichmuller gave an example of a hyperbolic simply connected Riemann surface whose mean excess is zero, disproving the first of these implications. We give an example of a simply connected parabolic Riemann surface with negative mean excess, thus disproving the other part. We also construct an example of a complete, simply connected, parabolic surface with nowhere positive curvature such that the integral of curvature in any disk about a fixed basepoint is less than -epsilon times the area of the disk, where epsilon > 0 is some constant. | |
| dc.description | 7 pages, 2 figures, LaTex | |
| dc.identifier | https://arxiv.org/abs/math/0209334 | |
| dc.identifier | http://arxiv.org/abs/math/0209334 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65068 | |
| dc.subject | Complex Variables | |
| dc.subject | 30F45 | |
| dc.title | A negative answer to Nevanlinna's type question and a parabolic surface with a lot of negative curvature | |
| dc.type | text |