Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry

Tamás Darvas; Chinh H Lu

doi:10.2140/gt.2020.24.1907

Abstract

We establish the essentially optimal form of Donaldson’s geodesic stability conjecture regarding existence of constant scalar curvature Kähler metrics. We carry this out by exploring in detail the metric geometry of Mabuchi geodesic rays, and the uniform convexity properties of the space of Kähler metrics.

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Tamás Darvas. Chinh H Lu. "Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry." Geom. Topol. 24 (4) 1907 - 1967, 2020. https://doi.org/10.2140/gt.2020.24.1907

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Received: 5 March 2019; Revised: 7 October 2019; Accepted: 4 November 2019; Published: 2020

First available in Project Euclid: 17 November 2020

zbMATH: 07274792

MathSciNet: MR4173924

Digital Object Identifier: 10.2140/gt.2020.24.1907

Subjects:

Primary: 32Q26 , 32U05 , 53C55

Keywords: Kähler metrics , Mabuchi rays , stability

Abstract

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