Pith. sign in

REVIEW 1 cited by

Optimal regularity for quasiminimal sets of codimension one in $\R^2$ and $\R^3$

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 2411.07210 v1 pith:7EWS2XMO submitted 2024-11-11 math.CA

Camille Labourie , Yana Teplitskaya This is my paper · ORCID
classification math.CA
keywords setsquasiminimallocallyseparateadditionareacodimensioncomponents
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

Quasiminimal sets are sets for which a pertubation can decrease the area but only in a controlled manner. We prove that in dimensions $2$ and $3$, such sets separate a locally finite family of local John domains. Reciprocally, we show that this property is a sufficient for quasiminimality. In addition, we show that quasiminimal sets locally separate the space in two components, except at isolated points in $\R^2$ or out a of subset of dimension strictly less than $N-1$ in $\R^N$.

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. Optimal regularity up to the boundary for Plateau-quasi-minimizers

    math.OC 2025-07 conditional novelty 7.0 of 10

    Plateau-quasi-minimizers in co-dimension one are characterized, up to the boundary, by bi-John domains with Ahlfors regular boundaries.

Pith tools