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

Darvas, Tamás; Lu, Chinh H

doi:10.2140/gt.2020.24.1907

Geodesic

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

Darvas, Tamás ¹ ; Lu, Chinh H ²

¹ Department of Mathematics, University of Maryland, College Park, MD, United States
² Laboratoire de Mathématiques d’Orsay, Univ. Paris-Sud, CNRS, Univ. Paris-Saclay, Orsay, France

Geometry & topology, Tome 24 (2020) no. 4, pp. 1907-1967.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

Résumé

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.

DOI : 10.2140/gt.2020.24.1907

Classification : 32Q26, 32U05, 53C55
Keywords: Kähler metrics, Mabuchi rays, stability

Affiliations des auteurs :

Darvas, Tamás ¹ ; Lu, Chinh H ²

¹ Department of Mathematics, University of Maryland, College Park, MD, United States
² Laboratoire de Mathématiques d’Orsay, Univ. Paris-Sud, CNRS, Univ. Paris-Saclay, Orsay, France

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     title = {Geodesic stability, the space of rays and uniform convexity in {Mabuchi} geometry},
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     year = {2020},
     doi = {10.2140/gt.2020.24.1907},
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}

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Darvas, Tamás; Lu, Chinh H. Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry. Geometry & topology, Tome 24 (2020) no. 4, pp. 1907-1967. doi : 10.2140/gt.2020.24.1907. http://geodesic.mathdoc.fr/articles/10.2140/gt.2020.24.1907/

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