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On the constant scalar curvature K\"ahler metrics, general automorphism group

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arxiv 1801.05907 v1 pith:RWLXJL72 submitted 2018-01-18 math.DG math.AP

Xiuxiong Chen , Jingrui Cheng This is my paper · ORCID
classification math.DGmath.AP
keywords csckcurvatureexistenceneq0scalarwhenahlerapplication
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abstract

In this paper, we derive estimates for scalar curvature type equations with more singular right hand side. As an application, we prove Donaldson's conjecture on the equivalence between geodesic stability and existence of cscK when $Aut_0(M,J)\neq0$. Moreover, we also show that when $Aut_0(M,J)\neq0$, the properness of $K$-energy with respect to a suitably defined distance implies the existence of cscK.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Analytic Bertini theorem II --- The local case

    math.AG 2026-07 accept novelty 8.0 of 10

    The local analytic Bertini theorem holds: multiplier ideal sheaves of psh functions on polydisc products restrict to fibers outside a pluripolar set.

  2. Long-time existence of some geometric flows with bounded scalar curvature

    math.DG 2026-06 unverdicted

    A survey reviewing the behavior of scalar curvature in Ricci flow, Kähler-Ricci flow with (1,1)-forms, and Laplacian flow.

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