Some remarks on conic degeneration and bending of Poincaré-Einstein metrics
| dc.creator | Mazzeo, Rafe | |
| dc.creator | Singer, Michael | |
| dc.date | 2007-09-10 | |
| dc.date.accessioned | 2026-07-07T08:28:42Z | |
| dc.date.available | 2026-07-07T08:28:42Z | |
| dc.description | Let $(M,g)$ be a compact Kähler-Einstein manifold with $c_1 > 0$. Denote by $K\to M$ the canonical line-bundle, with total space $X$, and $X_0$ the singular space obtained by blowing down $X$ along its zero section. We employ a construction by Page and Pope and discuss an interesting multi-parameter family of Poincaré--Einstein metrics on $X$. One 1-parameter subfamily $\{g_t\}_{t>0}$ has the property that as $t\searrow 0$, $g_t$ converges to a PE metric $g_0$ on $X_0$ with conic singularity, while $t^{-1}g_t$ converges to a complete Ricci-flat Kähler metric $\hat{g}_0$ on $X$. Another 1-parameters subfamily has an edge singularity along the zero section of $X$, with cone angle depending on the parameter, but has constant conformal infinity. These illustrate some unexpected features of the Poincaré-Einstein moduli space. | |
| dc.identifier | https://arxiv.org/abs/0709.1498 | |
| dc.identifier | http://arxiv.org/abs/0709.1498 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137708 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C25 | |
| dc.title | Some remarks on conic degeneration and bending of Poincaré-Einstein metrics | |
| dc.type | text |