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Mathematics > Differential Geometry

arXiv:0710.3919 (math)
[Submitted on 22 Oct 2007 (v1), last revised 2 Mar 2008 (this version, v2)]

Title:Bounding sectional curvature along a Kähler-Ricci flow

Authors:Wei-Dong Ruan, Yuguang Zhang, Zhenlei Zhang
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Abstract: If a normalized Kähler-Ricci flow $g(t),t\in[0,\infty),$ on a compact Kähler $n$-manifold, $n\geq 3$, of positive first Chern class satisfies $g(t)\in 2\pi c_{1}(M)$ and has $L^{n}$ curvature operator uniformly bounded, then the curvature operator will also uniformly bounded along the flow. Consequently the flow will converge along a subsequence to a Kähler-Ricci soliton.
Subjects: Differential Geometry (math.DG)
Cite as: arXiv:0710.3919 [math.DG]
  (or arXiv:0710.3919v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.3919

Submission history

From: Yuguang Zhang [view email]
[v1] Mon, 22 Oct 2007 03:18:35 UTC (7 KB)
[v2] Sun, 2 Mar 2008 02:26:00 UTC (10 KB)
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