Radial Balanced metrics on the unit disk
| dc.creator | Greco, Antonio | |
| dc.creator | Loi, Andrea | |
| dc.date | 2008-03-26 | |
| dc.date.accessioned | 2026-07-07T09:28:26Z | |
| dc.date.available | 2026-07-07T09:28:26Z | |
| dc.description | Let $Φ$ be a strictly plurisubharmonic and radial function on the unit disk ${\cal D}\subset {\complex}$ and let $g$ be the \K metric associated to the \K form $ω=\frac{i}{2}\partial\bar\partialΦ$. We prove that if $g$ is $g_{eucl}$-balanced of height 3 (where $g_{eucl}$ is the standard Euclidean metric on ${\complex}={\real}^2$), and the function $h(x)=e^{-Φ(z)}$, $x=|z|^2$, extends to an entire analytic function on ${\real}$, then $g$ equals the hyperbolic metric. The proof of our result is based on a interesting characterization of the function $f(x)=1-x$. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/0803.3711 | |
| dc.identifier | http://arxiv.org/abs/0803.3711 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157454 | |
| dc.subject | Differential Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 53D05, 53C55, 58C25, 58F06 | |
| dc.title | Radial Balanced metrics on the unit disk | |
| dc.type | text |