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arXiv · 1701.00306

K-energy on polarized compactifications of Lie groups

Yan Li·Bin Zhou·Xiaohua Zhu
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Abstract

In this paper, we study Mabuchi's K-energy on a compactification M of a reductive Lie group G, which is a complexification of its maximal compact subgroup K. We give a criterion for the properness of K-energy on the space of K \times K-invariant Kahler potentials. In particular, it turns to give an alternative proof of Delcroix's theorem for the existence of Kahler-Einstein metrics in case of Fano manifolds M . We also study the existence of minimizers of K-energy for general Kahler classes of M.

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Yan Li, Bin Zhou, Xiaohua Zhu. 2017-01-02. K-energy on polarized compactifications of Lie groups. https://arxiv.org/abs/1701.00306

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