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September 2017 Convergence of the $J$-flow on toric manifolds
Tristan C. Collins, Gábor Székelyhidi
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J. Differential Geom. 107(1): 47-81 (September 2017). DOI: 10.4310/jdg/1505268029

Abstract

We show that on a Kähler manifold whether the $J$-flow converges or not is independent of the chosen background metric in its Kähler class. On toric manifolds we give a numerical characterization of when the $J$-flow converges, verifying a conjecture in [19] (M. Lejmi and G. Székelyhidi, “The $J$-flow and stability”) in this case. We also strengthen existing results on more general inverse $\sigma_k$ equations on Kähler manifolds.

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Tristan C. Collins. Gábor Székelyhidi. "Convergence of the $J$-flow on toric manifolds." J. Differential Geom. 107 (1) 47 - 81, September 2017. https://doi.org/10.4310/jdg/1505268029

Information

Received: 2 July 2015; Published: September 2017
First available in Project Euclid: 13 September 2017

zbMATH: 06846961
MathSciNet: MR3698234
Digital Object Identifier: 10.4310/jdg/1505268029

Rights: Copyright © 2017 Lehigh University

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Vol.107 • No. 1 • September 2017
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