Relative Ding Stability and an Obstruction to the Existence of Mabuchi Solitons

Mabuchi solitons generalize Kähler–Einstein metrics on Fano manifolds, which constitute a Yau–Tian–Donaldson type correspondence with relative Ding stability. Comparing Kähler–Ricci solitons, there is distinct necessary condition for the existence. We show this can be implied by uniformly For this, we study inner product of $$\mathbb {C}^{*}$$ -actions equivariant test-configurations and obtain an integration formula over total space. To analyze uniform stability, adapting Okounkov body construction to setting torus action, give convex-geometry description reduced non-Archimedean J-functionals.