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Approximation of weak geodesics and subharmonicity of Mabuchi energy
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 25 (2016) no. 5, pp. 935-957.

In this paper we are interested in the approximation of weak geodesics connecting two Kähler metrics in the same cohomology class. As a consequence, we derive the convexity of the Mabuchi energy along geodesics. This important result was obtained recently by Berman-Berndtsson, and our approach can be seen as a “global version” of their original proof.

Dans cet article nous obtenons des résultats concernant l’approximation des géodésiques qui connectent deux métriques kähleriennes dans la même classe de cohomologie. Comme corollaire, nous obtenons une preuve de la convexité de la fonctionnelle de Mabuchi le long des géodésiques. C’est un théorème obtenu récemment par Berman-Berndtsson, et nos arguments représentent une version « globale » de leur démonstration originale.

Published online:
DOI: 10.5802/afst.1516
XiuXiong Chen 1; Long Li 2; Mihai Păuni 3

1 Department of Mathematics, Stony Brook University, NY, USA.
2 Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4K1, Canada.
3 Korea Institute for Advanced Study, School of Mathematics, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722, Korea.
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XiuXiong Chen; Long Li; Mihai Păuni. Approximation of weak geodesics and subharmonicity of Mabuchi energy. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 25 (2016) no. 5, pp. 935-957. doi : 10.5802/afst.1516. https://afst.centre-mersenne.org/articles/10.5802/afst.1516/

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