Soliton-type metrics and Kähler-Ricci flow on symplectic quotients
| dc.creator | La Nave, Gabriele | |
| dc.creator | Tian, Gang | |
| dc.date | 2009-03-13 | |
| dc.date.accessioned | 2026-07-07T12:52:25Z | |
| dc.date.available | 2026-07-07T12:52:25Z | |
| dc.description | In this paper, we first show an interpretation of the Kähler-Ricci flow on a manifold $X$ as an exact elliptic equation of Einstein type on a manifold $M$ of which $X$ is one of the (Kähler) symplectic reductions via a (non-trivial) torus action. There are plenty of such manifolds (e.g. any line bundle on $X$ will do). Such an equation is called $V$-soliton equation, which can be regarded as a generalization of Kähler-Einstein equations or Kähler-Ricci solitons. As in the case of Kähler-Einstein metrics, we can also reduce the $V$-soliton equation to a scalar equation on Kähler potentials, which is of Monge-Ampere type. We then prove some preliminary results towards establishing existence of solutions for such a scalar equation on a compact Kähler manifold $M$. One of our motivations is to apply the interpretation to studying finite time singularities of the Kähler-Ricci flow. | |
| dc.identifier | https://arxiv.org/abs/0903.2413 | |
| dc.identifier | http://arxiv.org/abs/0903.2413 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223287 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.title | Soliton-type metrics and Kähler-Ricci flow on symplectic quotients | |
| dc.type | text |