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Mabuchi metrics and properness of the modified DING functional

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arxiv 1709.03029 v1 pith:3M3VIIK6 submitted 2017-09-10 math.DG

Yan Li , Bin Zhou This is my paper · ORCID
classification math.DG
keywords mabuchimetricspropernessdingfanofunctionalgroupmodified
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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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  1. Relative Ding Stability and an Obstruction to the Existence of Mabuchi Solitons

    math.DG 2019-08 conditional novelty 7.0 of 10

    Uniform relative Ding stability of a Fano manifold implies the necessary numerical condition ϑ(M) < 1 for the existence of Mabuchi solitons.

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