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arXiv · 1709.03029

Mabuchi metrics and properness of the modified DING functional

Yan Li·Bin Zhou
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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.

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Yan Li, Bin Zhou. 2017-09-10. Mabuchi metrics and properness of the modified DING functional. https://arxiv.org/abs/1709.03029

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