In this work we study the intrinsic geometry of the space of Kahler metrics under various Riemannian metrics. The first part is on the Dirichlet metric. We motivate its study, we compute its curvature, and we make links with the Calabi metric, the K-energy, the degenerate complex Hessian equation. The second part is on the weighted metrics, for which we investigate as well their geometric properties.
The Dirichlet and the weighted metrics for the space of Kaehler metrics / Simone, Calamai; Kai, Zheng. - In: MATHEMATISCHE ANNALEN. - ISSN 1432-1807. - STAMPA. - 363:(2015), pp. 817-856. [10.1007/s00208-015-1188-x]
The Dirichlet and the weighted metrics for the space of Kaehler metrics
Simone, Calamai;
2015
Abstract
In this work we study the intrinsic geometry of the space of Kahler metrics under various Riemannian metrics. The first part is on the Dirichlet metric. We motivate its study, we compute its curvature, and we make links with the Calabi metric, the K-energy, the degenerate complex Hessian equation. The second part is on the weighted metrics, for which we investigate as well their geometric properties.
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