K-energy on polarized compactifications of Lie groups
Differential Geometry
2017-01-03 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1701.00306,
title = {K-energy on polarized compactifications of Lie groups},
author = {Yan Li and Bin Zhou and Xiaohua Zhu},
journal= {arXiv preprint arXiv:1701.00306},
year = {2017}
}
Comments
40pages, 4 figures