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

Darvas, Tamás; Lu, Chinh H

doi:10.2140/gt.2020.24.1907

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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

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.

Keywords

Kähler metrics, Mabuchi rays, stability

Mathematical Subject Classification 2010

Primary: 32Q26, 32U05, 53C55

References

Publication

Received: 5 March 2019

Revised: 7 October 2019

Accepted: 4 November 2019

Published: 10 November 2020

Proposed: John Lott

Seconded: Simon Donaldson, Bruce Kleiner

Authors

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 Orsay France

Volume 24, issue 4 (2020)