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Edge-Isoperimetric Inequality.pdf

DavoliPiovanoStefanelli_Triangular21Feb.pdf
Preview of Edge-Isoperimetric Inequality
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Summary

The Edge-Isoperimetric Problem (EIP) on the triangular lattice is characterized by introducing a suitable notion of perimeter and area, and EIP minimizers are shown to be extremizers of an isoperimetric inequality, attaining maximal area and minimal perimeter among connected configurations. The maximal area and minimal perimeter are explicitly quantified in terms of n, and minimizers are estimated to deviate from hexagonal configurations by at most Kt n3/4 + o(n3/4) points, with the constant Kt explicitly determined and shown to be sharp.

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Description

The Edge-Isoperimetric Problem (EIP) on the triangular lattice is characterized by introducing a suitable notion of perimeter and area, and EIP minimizers are...

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  • File Format: PDF
  • File Size: 1.1 MB
  • Pages: 28
  • Language: EN
  • Total Downloads: 112
  • Last Updated: 3 weeks ago

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