Pith. sign in

REVIEW 2 cited by

Quantitative stratification for the fractional Allen-Cahn equation and stationary nonlocal minimal surface

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 2503.16829 v1 pith:NPXYQ3DK submitted 2025-03-21 math.AP math.DG

Kelei Wang , Juncheng Wei , Ke Wu This is my paper · ORCID
classification math.APmath.DG
keywords allen-cahnequationfractionalquantitativecintiestimateestimatesminimal
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

We study properties of solutions to the fractional Allen-Cahn equation when $s\in (0, 1/2)$ and dimension $n\geq 2$. By applying the quantitative stratification principle developed by Naber and Valtorta, we obtain an optimal quantitative estimate on the transition set. As an application of this estimate, we improve the potential energy estimates of Cabre, Cinti, and Serra (2021), providing sharp versions for the fractional Allen-Cahn equation. Similarly, we obtain optimal perimeter estimates for stationary nonlocal minimal surfaces, extending previous results of Cinti, Serra, and Valdinoci (2019) from the stable case.

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. Improved convergence of Landau-de Gennes minimizers in the vanishing elasticity limit

    math.AP 2025-07 conditional novelty 6.0 of 10

    Landau-de Gennes minimizers converge in L^p for 1<p<∞ with sharp ε^3 bulk-energy decay in the vanishing elasticity limit.

  2. Stratification and rectifiability of harmonic map flows via tangent measures

    math.AP 2025-04 conditional novelty 6.0 of 10

    For suitable harmonic map flows, every time slice of the singular set is (n-2)-rectifiable with uniform Minkowski content estimates, and excluding harmonic and quasi-harmonic 2-spheres yields a sharp L^{3,∞} bound on ...

Pith tools