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2019 Coupled Kähler–Ricci solitons on toric Fano manifolds
Jakob Hultgren
Anal. PDE 12(8): 2067-2094 (2019). DOI: 10.2140/apde.2019.12.2067

Abstract

We prove a necessary and sufficient condition in terms of the barycenters of a collection of polytopes for existence of coupled Kähler–Einstein metrics on toric Fano manifolds. This confirms the toric case of a coupled version of the Yau–Tian–Donaldson conjecture and as a corollary we obtain an example of a coupled Kähler–Einstein metric on a manifold which does not admit Kähler–Einstein metrics. We also obtain a necessary and sufficient condition for existence of torus-invariant solutions to a system of soliton-type equations on toric Fano manifolds.

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Jakob Hultgren. "Coupled Kähler–Ricci solitons on toric Fano manifolds." Anal. PDE 12 (8) 2067 - 2094, 2019. https://doi.org/10.2140/apde.2019.12.2067

Information

Received: 9 April 2018; Accepted: 18 October 2018; Published: 2019
First available in Project Euclid: 14 December 2019

zbMATH: 07143410
MathSciNet: MR4023975
Digital Object Identifier: 10.2140/apde.2019.12.2067

Subjects:
Primary: 32Q15, 32Q20, 32Q26, 53C25

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 8 • 2019
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