The J-flow on Kahler surfaces: a boundary case

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.

12 pages, final version to appear in Analysis & PDE

References in corpus (2)

• Viscosity solutions to degenerate Complex Monge-Ampère equations
• Unstable products of smooth curves

Cited by in corpus (6)

• A viscosity approach to the Dirichlet problem for degenerate complex Hessian type equations
• Optimal lower bounds for Donaldson's J-functional
• $I$-properness of Mabuchi's $K$-energy
• Collapsing of the line bundle mean curvature flow on Kähler surfaces
• Monge-Ampère type equations on almost Hermitian manifolds
• Twisted and coupled constant scalar curvature Kähler metrics on minimal ruled surfaces