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arXiv · 1810.04661

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

Tamás Darvas·Chinh H. Lu
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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.

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Tamás Darvas, Chinh H. Lu. 2018-10-10. Geodesic stability, the space of rays, and uniform convexity in Mabuchi geometry. https://doi.org/10.2140/gt.2020.24.1907

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