Sharp \(N^{3/4}\) law for the minimizers of the edge-isoperimetric problem on the triangular lattice

DOI10.1007/s00332-016-9346-1zbMath1383.82063OpenAlexW2547130799WikidataQ40958042 ScholiaQ40958042MaRDI QIDQ683954

Paolo Piovano, Ulisse Stefanelli, Elisa Davoli

Publication date: 9 February 2018

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00332-016-9346-1

zbMATH Keywords

isoperimetric inequalitytriangular latticeWulff shape\(N^{3/4}\) lawedge perimeteredge-isoperimetric problem

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Statistical mechanics of crystals (82D25) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (22)

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Cites Work

• Continuum limit of total variation on point clouds
• Face-centered cubic crystallization of atomistic configurations
• On the crystallization of 2D hexagonal lattices
• A proof of crystallization in two dimensions
• The crystallization conjecture: a review
• A mass transportation approach to quantitative isoperimetric inequalities
• A selection principle for the sharp quantitative isoperimetric inequality
• Crystallization in carbon nanostructures
• The sharp quantitative isoperimetric inequality
• Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff shape
• Ground states of the 2D sticky disc model: fine properties and \(N^{3/4}\) law for the deviation from the asymptotic Wulff shape
• Wulff shape emergence in graphene
• Finite crystallization in the square lattice
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