Abstract
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.
Citation
Hao Fang. Mijia Lai. Jian Song. Ben Weinkove. "The $J$-flow on Kähler surfaces: a boundary case." Anal. PDE 7 (1) 215 - 226, 2014. https://doi.org/10.2140/apde.2014.7.215
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