The J-flow on Kahler surfaces: a boundary case
Differential Geometry
2016-01-20 v2
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.
Keywords
Cite
@article{arxiv.1204.4068,
title = {The J-flow on Kahler surfaces: a boundary case},
author = {Hao Fang and Mijia Lai and Jian Song and Ben Weinkove},
journal= {arXiv preprint arXiv:1204.4068},
year = {2016}
}
Comments
12 pages, final version to appear in Analysis & PDE