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PreprintCC BY 4.0arXiv

The relative isoperimetric profile of a unit square with a central square removed

  • Kyle Byassee
  • Hunter Johnson
  • Brandon Jones
  • Ezra Nance
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Abstract

We calculate the exact values of the relative isoperimetric profile for a unit square with a central square removed. In other words, given a removed central square of a fixed size, we provide a function which produces the smallest relative perimeter which bounds any possible area within this shape.

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Cite

BibTeXRIS
BibTeX
@misc{byassee2026relative,
  title = {{The relative isoperimetric profile of a unit square with a central square removed}},
  author = {Kyle Byassee and Hunter Johnson and Brandon Jones and Ezra Nance},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32946},
  eprint = {2609.32946},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32946},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The relative isoperimetric profile of a unit square with a central square removed
AU  - Kyle Byassee
AU  - Hunter Johnson
AU  - Brandon Jones
AU  - Ezra Nance
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32946
UR  - https://arxiv.org/abs/2609.32946
AB  - We calculate the exact values of the relative isoperimetric profile for a unit square with a central square removed. In other words, given a removed central square of a fixed size, we provide a function which produces the smallest relative perimeter which bounds any possible area within this shape.
ER  -