@article{Li2023, 
author = {Yan Li and Gang Tian and Xiaohua Zhu},
title = {Singular Kähler-Einstein metrics on        Q  -Fano compactifications of Lie groups},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {2},
pages = {1-43},
keywords = {Kähler-Einstein metrics, Q-Fano compactifications of Lie groups, variation method, reduced Ding functional, K-stability},
url = {https://www.sciopen.com/article/10.3934/mine.2023028},
doi = {10.3934/mine.2023028},
abstract = {In this paper, we prove an existence result for Kähler-Einstein metrics on        Q  -Fano compactifications of Lie groups by the variational method, provided their moment polytopes satisfy a fine condition. As an application, we prove that there is no        Q  -Fano              S      O        4    (      C    )-compactification which admits a Kähler-Einstein metric with the same volume as that of a smooth K-unstable Fano              S      O        4    (      C    )-compactification.}
}