Convergence properties of the Yang-Mills flow on Kaehler surfaces

dc.creatorDaskalopoulos, Georgios D.
dc.creatorWentworth, Richard A.
dc.date2004-10-04
dc.date.accessioned2026-07-07T05:12:50Z
dc.date.available2026-07-07T05:12:50Z
dc.descriptionLet $E$ 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.description30 pages. To appear in Crelle's Journal
dc.identifierhttps://arxiv.org/abs/math/0410055
dc.identifierhttp://arxiv.org/abs/math/0410055
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72731
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject58E15, 81T13
dc.titleConvergence properties of the Yang-Mills flow on Kaehler surfaces
dc.typetext

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