A variational proof for the existence of a conformal metric with preassigned negative Gaussian curvature for compact Riemann surfaces of genus $>1$
| dc.creator | Dey, Rukmini | |
| dc.date | 2001-12-19 | |
| dc.date | 2006-05-09 | |
| dc.date.accessioned | 2026-07-07T06:35:27Z | |
| dc.date.available | 2026-07-07T06:35:27Z | |
| dc.description | Given an smooth function $K <0$ we prove a result by Berger, Kazhdan and others that in every conformal class there exists a metric which attains this function as its Gaussian curvature for a compact Riemann surface of genus $g>1$. We do so by minimizing an appropriate functional using elementary analysis. In particular for $K$ a negative constant, this provides an elementary proof of the uniformization theorem for compact Riemann surfaces of genus $g >1$. | |
| dc.description | 9 pages, AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0112203 | |
| dc.identifier | http://arxiv.org/abs/math/0112203 | |
| dc.identifier | Corrected Version to: Proc. Ind. Academy of Sciences, 111 (2001), 407 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99799 | |
| dc.subject | Differential Geometry | |
| dc.title | A variational proof for the existence of a conformal metric with preassigned negative Gaussian curvature for compact Riemann surfaces of genus $>1$ | |
| dc.type | text |