Isoperimetric stability in lattices

Ben Barber, Joshua Erde, Peter Keevash, Alexander Roberts

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)5021-5029
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number12
Early online date2023
Publication statusE-pub ahead of print - 2023


  • Isoperimetry
  • Stability
  • Convex Geometry

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)

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