Compactness results for the Kähler-Ricci flow
| dc.creator | Sesum, Natasa | |
| dc.date | 2007-07-19 | |
| dc.date | 2007-09-23 | |
| dc.date.accessioned | 2026-07-07T08:31:12Z | |
| dc.date.available | 2026-07-07T08:31:12Z | |
| dc.description | We consider the Kähler-Ricci flow $\frac{\partial}{\partial t}g_{i\bar{j}} = g_{i\bar{j}} - R_{i\bar{j}}$ on a compact Kähler manifold $M$ with $c_1(M) > 0$, of complex dimension $k$. We prove the $ε$-regularity lemma for the Kähler-Ricci flow, based on Moser's iteration. Assume that the Ricci curvature and $\int_M |\rem|^k dV_t$ are uniformly bounded along the flow. Using the $ε$-regularity lemma we derive the compactness result for the Kähler-Ricci flow. Under our assumptions, if $k \ge 3$ in addition, using the compactness result we show that $|\rem| \le C$ holds uniformly along the flow. This means the flow does not develop any singularities at infinity. We use some ideas of Tian from \cite{Ti} to prove the smoothing property in that case. | |
| dc.identifier | https://arxiv.org/abs/0707.2974 | |
| dc.identifier | http://arxiv.org/abs/0707.2974 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138438 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C44 | |
| dc.title | Compactness results for the Kähler-Ricci flow | |
| dc.type | text |