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The $J$-flow on Kähler
surfaces: a boundary case
Hao Fang, Mijia Lai, Jian Song and Ben Weinkove |
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Vol. 7 (2014), No. 1, 215–226
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Abstract |
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We study the -flow on Kähler surfaces when the Kähler class lies on the boundary of the open cone for which global smooth convergence holds and satisfies a nonnegativity condition. We obtain a estimate and show that the -flow converges smoothly to a singular Kähler metric away from a finite number of curves of negative self-intersection on the surface. We discuss an application to the Mabuchi energy functional on Kähler surfaces with ample canonical bundle. |
Keywords
Kähler, $J$-flow, complex Monge–Ampère
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Mathematical Subject Classification 2010
Primary: 53C44, 53C55
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Milestones
Received: 9 January 2013
Accepted: 22 August 2013
Published: 7 May 2014
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Authors |
| Hao Fang | |
| Department of Mathematics University of Iowa Iowa City, IA 52242 United States |
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| Mijia Lai | |
| Department of Mathematics University of Rochester Rochester, NY 14642 United States |
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| Jian Song | |
| Department of Mathematics Rutgers University Piscataway, NJ 08854 United States |
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| Ben Weinkove | |
| Mathematics Department Northwestern University Evanston, IL 60208 United States |
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