We prove a sharp quantitative version of Hales' isoperimetric honeycomb theorem by exploiting a quantitative isoperimetric inequality for polygons and an improved convergence theorem for planar bubble clusters. Further applications include the description of isoperimetric tilings of the torus with respect to almost unit-area constraints or with respect to almost flat Riemannian metrics.

A sharp quantitative version of Hales' isoperimetric honeycomb theorem

Caroccia M.;
2016-01-01

Abstract

We prove a sharp quantitative version of Hales' isoperimetric honeycomb theorem by exploiting a quantitative isoperimetric inequality for polygons and an improved convergence theorem for planar bubble clusters. Further applications include the description of isoperimetric tilings of the torus with respect to almost unit-area constraints or with respect to almost flat Riemannian metrics.
2016
Hales' honeycomb theorem
Isoperimetric problems
Partitioning problems
File in questo prodotto:
File Dimensione Formato  
A sharp quantitative version of Hales’ isoperimetric honeycomb theorem.pdf

Accesso riservato

: Publisher’s version
Dimensione 526.08 kB
Formato Adobe PDF
526.08 kB Adobe PDF   Visualizza/Apri
11311-1174054_Caroccia.pdf

accesso aperto

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 298.99 kB
Formato Adobe PDF
298.99 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1174054
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 5
social impact