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.

0 0
·
0 Bookmarks
·
23 Views

### 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