The J-flow on Kähler surfaces: A boundary case

Hao Fang; Mijia Lai; Jian Song; Ben Weinkove

doi:10.2140/apde.2014.7.215

The J-flow on Kähler surfaces: A boundary case

Hao Fang, Mijia Lai, Jian Song, Ben Weinkove

Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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.

Original language	English (US)
Pages (from-to)	215-226
Number of pages	12
Journal	Analysis and PDE
Volume	7
Issue number	1
DOIs	https://doi.org/10.2140/apde.2014.7.215
State	Published - 2014

Keywords

Complex monge-ampère
J-flow
Kähler

ASJC Scopus subject areas

Analysis
Numerical Analysis
Applied Mathematics

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10.2140/apde.2014.7.215

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abstract = "We study the J-flow on K{\"a}hler surfaces when the K{\"a}hler 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 K{\"a}hler 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 K{\"a}hler surfaces with ample canonical bundle.",

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T2 - A boundary case

AU - Fang, Hao

AU - Lai, Mijia

AU - Song, Jian

AU - Weinkove, Ben

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Complex monge-ampère

KW - J-flow

KW - Kähler

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JO - Analysis and PDE

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ER -

The J-flow on Kähler surfaces: A boundary case

Abstract

Keywords

ASJC Scopus subject areas

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