Pith. sign in

REVIEW 2 cited by

Scalar curvature rigidity of degenerate warped product spaces

Not yet reviewed by Pith; the record is open.

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 2306.05413 v3 pith:4FQIKJYX submitted 2023-06-08 math.DG

classification math.DG
keywords curvaturedegenerateproductrigidityscalarspaceswarpedextremality
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

In this paper we prove the scalar curvature extremality and rigidity for a class of warped product spaces that are possibly degenerate at the two ends. The leaves of these warped product spaces can be any closed Riemannian manifolds with nonnegative curvature operators and nonvanishing Euler characteristics, flat tori, round spheres and their direct products. In particular, we obtain the scalar curvature extremality and rigidity for certain degenerate toric bands and also for round spheres with two antipodal points removed. This answers positively the corresponding questions of Gromov in all dimensions.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Gap phenomenon for scalar curvature

    math.DG 2025-01 conditional novelty 6.0 of 10

    Scalar curvature on any closed even-dimensional manifold with nonzero Euler characteristic can be increased by at most an explicit constant, the gap, which is a function of the minimal eigenvalue of the curvature oper...

  2. Scalar curvature rigidity of parabolically convex domains in hyperbolic spaces

    math.DG 2024-11 reject novelty 6.0 of 10

    A nonzero-degree map into a parabolically convex hyperbolic domain, with scalar curvature and boundary curvature bounds, forces the domain to be hyperbolic and the boundary map to be an isometry.

Pith tools