Article

The J-flow on Kahler surfaces: a boundary case

04/2012;
Source: arXiv

ABSTRACT 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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Keywords

C^0 estimate
 
curves
 
J-flow converges
 
Kahler class
 
Kahler surfaces
 
Mabuchi energy functional
 
negative self-intersection
 
nonnegativity condition
 
open cone
 
singular Kahler metric