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Creators/Authors contains: "Shi, Yalong"

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  1. ; ; ; (, J. Reine Angew. Math. 820 (2025), 153–165.)
    Accepted Manuscript Full Text Available
  2. ; ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract Let 𝑋 be a Kähler manifold with semiample canonical bundle K X K_{X}.It is proved in [W. Jian, Y. Shi and J. Song, A remark on constant scalar curvature Kähler metrics on minimal models,Proc. Amer. Math. Soc.147(2019), 8, 3507–3513] that, for any Kähler class 𝛾, there exists δ > 0 \delta>0such that, for all t ∈ ( 0 , δ ) t\in(0,\delta), there exists a unique cscK metric g t g_{t}in K X + t ⁢ γ K_{X}+t\gamma.In this paper, we prove that { ( X , g t ) } t ∈ ( 0 , δ ) \{(X,g_{t})\}_{t\in(0,\delta)}have uniformly bounded Kähler potentials, volume forms and diameters.As a consequence, these metric spaces are pre-compact in the Gromov–Hausdorff sense. 
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