2019/08/31 by Yi Yao · 1 citation
Mathematics · #Advanced Algebra and Geometry #Computer science #Differential geometry #Equivariant map #Fano plane #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Mathematical analysis #Mathematics #Pure mathematics #Regular polygon #Space (punctuation) #Stability (learning theory) #Torus #math.DG #msc:14D06 #msc:32Q15 #msc:32Q20
paper · pdf · doi:10.1007/s12220-021-00858-z
40 pages, 1 figure. Final version. To appear in J. Geom. Anal
openalex created_date 2019/08/29 · openalex publication_date 2022/01/29 · arxiv created 2022/01/30 · arxiv updated 2022/02/01 · openalex updated_date 2026/08/05
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 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.