Mabuchi metrics and properness of the modified DING functional
Differential Geometry
2017-09-12 v1
Abstract
In this paper, we study Mabuchi metrics on Fano manifolds. We prove that Mabuchi metrics exist if the modified Ding functional is proper modulo a reductive subgroup of its automorphism group. On the other hand, the inverse that Mabuchi metrics implies the properness is obtained by using Darvas-Rubinstein's properness principle. As an application, we establish a criterion for the existence of Mabuchi metrics on Fano group compactifications.
Keywords
Cite
@article{arxiv.1709.03029,
title = {Mabuchi metrics and properness of the modified DING functional},
author = {Yan Li and Bin Zhou},
journal= {arXiv preprint arXiv:1709.03029},
year = {2017}
}