Isoperimetric stability in lattices

Ben Barber; Joshua Erde; Peter Keevash; Alexander Roberts

doi:10.1090/proc/16439

Isoperimetric stability in lattices

Ben Barber, Joshua Erde, Peter Keevash, Alexander Roberts

Institut für Diskrete Mathematik (5050)

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

Abstract

We obtain isoperimetric stability theorems for general Cayley digraphs on Zd. For any fixed B that generates Zd over Z, we characterise the approximate structure of large sets A that are approximately isoperimetric in the Cayley digraph of B: we show that A must be close to a set of the form kZ ∩ Zd, where for the vertex boundary Z is the conical hull of B, and for the edge boundary Z is the zonotope generated by B.

Originalsprache	englisch
Seiten (von - bis)	5021-5029
Seitenumfang	9
Fachzeitschrift	Proceedings of the American Mathematical Society
Jahrgang	151
Ausgabenummer	12
Frühes Online-Datum	2023
DOIs	https://doi.org/10.1090/proc/16439
Publikationsstatus	Veröffentlicht - 1 Dez. 2023

ASJC Scopus subject areas

Angewandte Mathematik
Allgemeine Mathematik

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10.1090/proc/16439

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KW - Convex Geometry

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Isoperimetric stability in lattices

Abstract

ASJC Scopus subject areas

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