Analysis & PDE

  • Anal. PDE
  • Volume 7, Number 1 (2014), 215-226.

The $J$-flow on Kähler surfaces: a boundary case

Hao Fang, Mijia Lai, Jian Song, and Ben Weinkove

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We study the J-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 C0 estimate and show that the J-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.

Article information

Anal. PDE, Volume 7, Number 1 (2014), 215-226.

Received: 9 January 2013
Accepted: 22 August 2013
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]

Kähler $J$-flow complex Monge–Ampère


Fang, Hao; Lai, Mijia; Song, Jian; Weinkove, Ben. The $J$-flow on Kähler surfaces: a boundary case. Anal. PDE 7 (2014), no. 1, 215--226. doi:10.2140/apde.2014.7.215.

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