Pith. sign in

REVIEW 1 cited by

Poincar\'{e} inequality and energy of separating sets

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 2401.02762 v1 pith:SRHU6YSX submitted 2024-01-05 math.MG math.DGmath.FA

Emanuele Caputo , Nicola Cavallucci This is my paper · ORCID
classification math.MGmath.DGmath.FA
keywords inequalitypoincarseparatingenergypropertiessetstermsapproximate
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We study geometric characterizations of the Poincar\'{e} inequality in doubling metric measure spaces in terms of properties of separating sets. Given a couple of points and a set separating them, such properties are formulated in terms of several possible notions of energy of the boundary, involving for instance the perimeter, codimension type Hausdorff measures, capacity, Minkowski content and approximate modulus of suitable families of curves. We prove the equivalence within each of these conditions and the $1$-Poincar\'e inequality.

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. Geometric characterizations of ${\sf PI}$ spaces: an overview of some modern techniques

    math.MG 2025-01 conditional novelty 2.0 of 10

    The paper reviews and partly re-proves results showing that a doubling metric measure space is a PI space if and only if its separating sets have enough weighted boundary energy.

Pith tools