Mabuchi metrics and properness of the modified DING functional

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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• Generalized Kähler Einstein metrics and uniform stability for toric Fano manifolds
• The Weyl Integration Model for KAK decomposition of Reductive Lie Group
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Cited by in corpus (7)

• Mabuchi Solitons and Relative Ding Stability of Toric Fano Varieties
• Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds
• The inverse Monge-Ampere flow and applications to Kahler-Einstein metrics
• Relative Ding Stability and an Obstruction to the Existence of Mabuchi Solitons
• Relative Ding and $K$-stability of toric Fano manifolds in low dimensions
• Remarks on modified Ding functional for toric Fano manifolds
• $G$-Sasaki manifolds and K-energy