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Mabuchi's soliton metric and relative D-stability

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arxiv 1905.05948 v2 pith:CCCOLBHJ submitted 2019-05-15 math.DG math.CV

Tomoyuki Hisamoto This is my paper · ORCID
classification math.DGmath.CV
keywords mabuchimetricfanoadmitsahler-einsteincharacterizedcriticald-stability
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For Fano manifolds T. Mabuchi introduced a generalization of the K\"ahler-Einstein metric, which is characterized as the critical point of the Ricci-Calabi functional. We show that a Fano manifold admits Mabuchi's metric if and only if it is uniformly relatively D-stable.

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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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