Convergence properties of the Yang-Mills flow on Kaehler surfaces
| dc.creator | Daskalopoulos, Georgios D. | |
| dc.creator | Wentworth, Richard A. | |
| dc.date | 2004-10-04 | |
| dc.date.accessioned | 2026-07-07T05:12:50Z | |
| dc.date.available | 2026-07-07T05:12:50Z | |
| dc.description | Let $E$ be a hermitian complex vector bundle over a compact Kähler surface $X$ with Kähler form $ω$, and let $D$ be an integrable unitary connection on $E$ defining a holomorphic structure $D^{\prime\prime}$ on $E$. We prove that the Yang-Mills flow on $(X,ω)$ with initial condition $D$ converges, in an appropriate sense which takes into account bubbling phenomena, to the double dual of the graded sheaf associated to the $ω$-Harder-Narasimhan-Seshadri filtration of the holomorphic bundle $(E,D^{\prime\prime})$. This generalizes to Kähler surfaces the known result on Riemann surfaces and proves, in this case, a conjecture of Bando and Siu. | |
| dc.description | 30 pages. To appear in Crelle's Journal | |
| dc.identifier | https://arxiv.org/abs/math/0410055 | |
| dc.identifier | http://arxiv.org/abs/math/0410055 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72731 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 58E15, 81T13 | |
| dc.title | Convergence properties of the Yang-Mills flow on Kaehler surfaces | |
| dc.type | text |