Open Access
Translator Disclaimer
2014 The $J$-flow on Kähler surfaces: a boundary case
Hao Fang, Mijia Lai, Jian Song, Ben Weinkove
Anal. PDE 7(1): 215-226 (2014). DOI: 10.2140/apde.2014.7.215

Abstract

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.

Citation

Download Citation

Hao Fang. Mijia Lai. Jian Song. Ben Weinkove. "The $J$-flow on Kähler surfaces: a boundary case." Anal. PDE 7 (1) 215 - 226, 2014. https://doi.org/10.2140/apde.2014.7.215

Information

Received: 9 January 2013; Accepted: 22 August 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1294.53060
MathSciNet: MR3219504
Digital Object Identifier: 10.2140/apde.2014.7.215

Subjects:
Primary: 53C44 , 53C55

Keywords: $J$-flow , complex Monge–Ampère , Kähler

Rights: Copyright © 2014 Mathematical Sciences Publishers

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.7 • No. 1 • 2014
MSP
Back to Top