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Singular scalar curvature equations

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arxiv 2205.14726 v1 pith:IE2BWUGI submitted 2022-05-29 math.DG math.AP

Kai Zheng This is my paper · ORCID
classification math.DGmath.AP
keywords curvaturemetricsscalarsingularahlerequationestimatesahler-einstein
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abstract

We develop estimates for the equation of scalar curvature of singular metrics with cone angle $\beta>1$, in a big and semi-positive cohomology class on a K\"ahler manifold. We further derive the Laplacian estimate for the scalar curvature equation of degenerate K\"ahler metrics. We then have several applications of these estimates on the singular constant scalar curvature K\"ahler metrics, which also include the singular K\"ahler-Einstein metrics.

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  1. Nash entropy, Calabi energy and geometric regularization of singular K\"ahler metrics

    math.DG 2025-02 conditional novelty 8.0 of 10

    Singular Kähler metrics with Ricci curvature bounded below and rational cohomology class induce non-collapsed RCD spaces homeomorphic to the projective variety, under a resolution condition on the anti-canonical bundle.

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