Geodesic stability, the space of rays, and uniform convexity in Mabuchi geometry
Differential Geometry
2020-11-18 v4 Complex Variables
Abstract
We establish the essentially optimal form of Donaldson's geodesic stability conjecture regarding existence of constant scalar curvature K\"ahler 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 K\"ahler metrics.
Keywords
Cite
@article{arxiv.1810.04661,
title = {Geodesic stability, the space of rays, and uniform convexity in Mabuchi geometry},
author = {Tamás Darvas and Chinh H. Lu},
journal= {arXiv preprint arXiv:1810.04661},
year = {2020}
}
Comments
v2: Changes in presentation. References added. v3: We show that approximation is possible with C^11 rays with converging radial K-energy. As an application, we prove the C^11 uniform geodesic stability conjecture. v4: we shifted the main focus of the paper towards geodesic stability, reflected in the presentation and a new title