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• W1566792340 abstract "Suppose $(X,omega)$ is a compact Kahler manifold. Following Mabuchi, the space of smooth Kahler potentials $mathcal H$ can be endowed with a Riemannian structure, which induces an infinite dimensional path length metric space $(mathcal H,d)$. We prove that the metric completion of $(mathcal H,d)$ can be identified with $(mathcal E^2(X,omega),tilde d)$, and this latter space is a complete non-positively curved geodesic metric space. In obtaining this result, we will rely on envelope techniques which allow for a treatment in a very general context. Profiting from this, we will characterize the pairs of potentials in $text{PSH}(X,omega)$ that can be connected by weak geodesics and we will also give a characterization of $mathcal E(X,omega)$ in this context." @default.
• W1566792340 created "2016-06-24" @default.
• W1566792340 creator A5006577864 @default.
• W1566792340 date "2014-01-28" @default.
• W1566792340 modified "2023-09-27" @default.
• W1566792340 title "The Mabuchi Completion of the Space of Kahler Potentials" @default.
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