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

Chinh H. Lu; Tam\'as Darvas

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

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arxiv 1810.04661 v4 pith:52Z3ADNV submitted 2018-10-10 math.DG math.CV

Tamás Darvas , Chinh H. Lu This is my paper · ORCID

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keywords geodesicahlerconvexitygeometrymabuchimetricsraysspace

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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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The metric geometry of singularity types
math.DG 2019-09 accept novelty 8.0 of 10

A new metric d_S on singularity types of θ-psh potentials is defined; on positive-mass classes it is complete, and it governs convergence of solutions and multiplier ideal sheaves.

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