Pith. sign in

REVIEW 1 cited by

Near equality in the two-dimensional Brunn-Minkowski inequality

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 1206.1965 v2 pith:NU2RQ5RB submitted 2012-06-09 math.CA

classification math.CA
keywords nearlyinequalitysetsbrunn-minkowskiequalitypairtwo-dimensionalachieves
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

If a pair of subsets of two-dimensional Euclidean space nearly achieves equality in the Brunn-Minkowski inequality, in the sense that the measure of the associated sumset is nearly equal to the lower bound provided by the inequality, then these sets must nearly coincide with a pair of homothetic convex sets. The proof relies on a continuum analogue of a theorem of Freiman which characterizes finite sets of integers whose sumsets are of nearly minimal size. Small corrections and clarifications have been made in this draft.

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. Sharp Quantitative Stability for the Pr\'ekopa-Leindler and Borell-Brascamp-Lieb Inequalities

    math.FA 2025-01 conditional novelty 8.0 of 10

    Sharp quantitative stability for the Borell-Brascamp-Lieb inequality (and hence Prékopa-Leindler) is proven: near-equality of the integral implies an O(√δ) L1-distance to a p-concave function.

Pith tools