Pith. sign in

REVIEW 2 cited by

Rigidity results for free boundary hypersurfaces in initial data sets with boundary

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 2502.09433 v1 pith:YM4WSHKR submitted 2025-02-13 math.DG gr-qc

Deivid de Almeida , Abraão Mendes This is my paper
classification math.DGgr-qc
keywords boundaryfreedatainitialresultssetshypersurfacesextend
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

In this work, we present several rigidity results for compact free boundary hypersurfaces in initial data sets with boundary. Specifically, in the first part of the paper, we extend the local splitting theorems from [G. J. Galloway and H. C. Jang, Some scalar curvature warped product splitting theorems, Proc. Am. Math. Soc. 148 (2020), no. 6, 2617-2629] to the setting of manifolds with boundary. To achieve this, we build on the approach of the original paper, utilizing results on free boundary marginally outer trapped surfaces (MOTS) applied to specific initial data sets. In the second part, we extend the main results from [A. Barros and C. Cruz, Free boundary hypersurfaces with non-positive Yamabe invariant in mean convex manifolds, J. Geom. Anal. 30 (2020), no. 4, 3542-3562] to the context of free boundary MOTS in initial data sets with boundary.

Discussion (0). Sign in 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. Marginally outer trap surface with capillary boundary and rigidity of initial data sets

    math.DG 2025-07 reject novelty 6.0 of 10

    For stable MOTS with capillary boundary, equality in the area estimate forces the contact angle to 90 degrees and the ambient initial data set to split as a product, under stated energy assumptions.

  2. Area-charge inequality and local rigidity in charged initial data sets

    math.DG 2025-05 conditional novelty 5.0 of 10

    Equality in the area-charge inequality forces a spherical horizon to have a locally product geometry with constant normal electric and magnetic fields.

Pith tools