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

Tamás Darvas and Chinh H Lu

Geometry & Topology 24 (2020) 1907–1967

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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Kähler metrics, Mabuchi rays, stability
Mathematical Subject Classification 2010
Primary: 32Q26, 32U05, 53C55
Received: 5 March 2019
Revised: 7 October 2019
Accepted: 4 November 2019
Published: 10 November 2020
Proposed: John Lott
Seconded: Simon Donaldson, Bruce Kleiner
Tamás Darvas
Department of Mathematics
University of Maryland
College Park, MD
United States
Chinh H Lu
Laboratoire de Mathématiques d’Orsay
Univ. Paris-Sud, CNRS, Univ. Paris-Saclay