An isoperimetric inequality in the universal cover of the punctured plane

Noga Alon, Adi Pinchasi, Rom Pinchasi

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We find the largest ε{lunate} (approximately 1.71579) for which any simple closed path α in the universal cover over(R2 {set minus} Z2, ̃) of R2 {set minus} Z2, equipped with the natural lifted metric from the Euclidean two-dimensional plane, satisfies L (α) ≥ ε{lunate} A (α), where L (α) is the length of α and A (α) is the area enclosed by α. This generalizes a result of Schnell and Segura Gomis, and provides an alternative proof for the same isoperimetric inequality in R2 {set minus} Z2.

Original languageEnglish (US)
Pages (from-to)5691-5701
Number of pages11
JournalDiscrete Mathematics
Volume308
Issue number23
DOIs
StatePublished - Dec 6 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Keywords

  • Isoperimetric inequality
  • Universal covering space

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