Pith. sign in

REVIEW 4 cited by

K\"ahler families of Green's functions

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2405.17232 v2 pith:G37YZHYY submitted 2024-05-27 math.CV math.AGmath.APmath.DG

Vincent Guedj , Tat Dat Tô This is my paper · ORCID
classification math.CVmath.AGmath.APmath.DG
keywords ahlerfamiliesfunctionsgreenmetricsallowingapplyassociated
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

In a remarkable series of works, Guo, Phong, Song, and Sturm have obtained key uniform estimates for the Green's functions associated with certain K\"ahler metrics. In this note, we broaden the scope of their techniques by removing one of their assumptions and allowing the complex structure to vary. We apply our results to various families of canonical K\"ahler metrics.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

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

  1. On K\"ahler-Einstein Currents

    math.DG 2025-02 conditional novelty 8.0 of 10

    Singular Kähler-Einstein metrics on klt pairs define Kähler currents, and a tame approximation with L^p Ricci control suffices to make the metric completion an RCD space.

  2. 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.

  3. Estimates of heat kernels and Sobolev-type inequalities for twisted differential forms on compact K\"ahler manifolds

    math.CV 2025-07 conditional novelty 6.0 of 10

    The paper extends the Sobolev-type inequalities of Guo-Phong-Song-Sturm and Guedj-Tô from functions to twisted differential forms using heat kernel estimates.

  4. Uniform estimates: from Yau to Kolodziej

    math.DG 2025-02 accept novelty 6.0 of 10

    A new envelope-based reduction proves uniform a priori estimates from Yau's L^p bound, recovering and extending Kolodziej's Orlicz-type criterion.

Pith tools