Pith. sign in

REVIEW 1 cited by

New differential operator and non-collapsed $RCD$ spaces

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 1905.00123 v2 pith:Y2BIV4UC submitted 2019-04-30 math.DG math.MG

Shouhei Honda This is my paper · ORCID
classification math.DGmath.MG
keywords non-collapsedspacescompactapplicationassociatedcasecharacterizationscondition
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

We show characterizations of non-collapsed compact $RCD(K, N)$ spaces, which in particular confirm a conjecture of De Philippis-Gigli on the implication from the weakly non-collapsed condition to the non-collapsed one in the compact case. The key idea is to give the explicit formula of the Laplacian associated to the pull-back Riemannian metric by embedding in $L^2$ via the heat kernel. This seems the first application of geometric flow to the study of RCD spaces.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. On the structure of RCD spaces with upper curvature bounds

    math.DG 2019-08 accept novelty 8.0 of 10

    Every RCD space with curvature bounded above is a topological manifold with boundary whose interior is the regular set, a smooth geodesically convex manifold.

Pith tools