Convergence of Kaehler-Ricci flow with integral curvature bound
| dc.creator | Fang, Fuquan | |
| dc.creator | Zhang, Yuguang | |
| dc.date | 2007-07-24 | |
| dc.date.accessioned | 2026-07-07T08:19:52Z | |
| dc.date.available | 2026-07-07T08:19:52Z | |
| dc.description | Let $g(t)$, $t\in [0, +\infty)$, be a solution of the normalized Kähler-Ricci flow on a compact Kähler $n$-manifold $M$ with $c_{1}(M)>0$ and initial metric $g (0)\in 2πc_{1}(M)$. If there is a constant $C$ independent of $t$ such that $$ \int_{M}|Rm(g(t))|^{n}dv_{t}\leq C,$$ then, for any $t_{k}\to \infty$, a subsequence of $(M, g(t_{k}))$ converges to a compact orbifold $(X, h)$ with only finite many singular points $\{q_{j}\}$ in the Gromov-Hausdorff sense, where $h$ is a Kähler metric on $X\backslash \{q_{j}\}$ satisfying the Kähler-Ricci soliton equation, i.e. there is a smooth function $f$ such that $$Ric(h)-h=\nabla\bar{\nabla}f, {\rm and}\it \nabla \nabla f=\bar{\nabla} \bar{\nabla} f=0. $$ | |
| dc.identifier | https://arxiv.org/abs/0707.3470 | |
| dc.identifier | http://arxiv.org/abs/0707.3470 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134914 | |
| dc.subject | Differential Geometry | |
| dc.subject | Geometric Topology | |
| dc.title | Convergence of Kaehler-Ricci flow with integral curvature bound | |
| dc.type | text |