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arXiv · 1410.1821

$I$-properness of Mabuchi's $K$-energy

Kai Zheng
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Abstract

Over the space of Kähler metrics associated to a fixed Kähler class, we first prove the lower bound of the energy functional $\tilde E^β$, then we provide the criterions of the geodesics rays to detect the lower bound of $\tilde {\mathfrak J}^β$-functional. They are used to obtain the properness of Mabuchi's $K$-energy. The criterions are examined by showing the convergence of the negative gradient flow of $\tilde {\mathfrak J}^β$-functional.

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Kai Zheng. 2014-10-07. $I$-properness of Mabuchi's $K$-energy. https://doi.org/10.1007/s00526-015-0884-4

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