The J-flow on Kahler surfaces: a boundary case

Details The J-flow on Kahler surfaces: a boundary case The J-flow on Kahler surfaces: a boundary case

2012-04-18

arxiv.org/abs/1204.4068v1

Mathematics

Differential Geometry

11 pages

Scientific paper

We study the J-flow on Kahler surfaces when the Kahler class lies on the boundary of the open cone for which global smooth convergence holds, and satisfies a nonnegativity condition. We obtain a C^0 estimate and show that the J-flow converges smoothly to a singular Kahler 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 Kahler surfaces with ample canonical bundle.

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