English

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}
}