相对Ding稳定性和Mabuchi孤子存在的一个障碍
Relative Ding Stability and an Obstruction to the Existence of Mabuchi Solitons
摘要：
Mabuchi孤子推广了Fano流形上的Kähler-Einstein度量，构成了具有相对Ding稳定性的Yau-Tian-Donaldson型对应.与Kähler-Ricci孤子相比，存在一个明显的必要条件。我们证明了这个条件可以由一致相对Ding稳定性所隐含。为此，我们研究了$\mathbb{C}^{*}$ -作用在等变检验构形上的内积，得到了全空间上的积分公式。为了分析系统的一致稳定性，通过调整Okounkov体的构造，使之适应于环面作用量的设置，给出了约化非阿基米德J-泛函的凸几何描述.
英文摘要：
Mabuchi solitons generalize Kähler-Einstein metrics on Fano manifolds, which constitute a Yau-Tian-Donaldson type correspondence with relative Ding stability. Comparing with Kähler-Ricci solitons, there is a distinct necessary condition for the existence. We show this condition can be implied by the uniformly relative Ding stability. For this we study the inner product of $\mathbb{C}^{*}$-actions on equivariant test-configurations and obtain an integration formula over the total space. To analyze the uniform stability, by adapting Okounkov body construction to the setting of torus action, we give a convex-geometry description for the reduced non-Archimedean J-functionals.
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