Mabuchi metrics and properness of the modified Ding functional
Mabuchi metrics and properness of the modified Ding functional
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DOI：
10.2140/pjm.2019.302.659
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发表时间：
2017-09
影响因子：
0.6
通讯作者：
Yan Li;Bin Zhou
中科院分区：
文献类型：
--
作者：
Yan Li;Bin Zhou
本文研究了Fano流形上的Mabuchi度量。我们证明了如果修正的Ding泛函是其自同构群的约化子群的真模，则存在Mabuchi度量。另一方面，利用达瓦斯-鲁宾斯坦的适定性原理得到了Mabuchi度量蕴含适当性的逆。作为应用，我们建立了Fano群紧化上Mabuchi度量存在的一个判据。
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.