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PreprintarXiv licencearXiv

A comparison theorem for the planar strip isoperimetric problem

  • Skilyn Leon
  • Rosa Pavlak
  • Evelyn Pulla
  • Xi Sisi Shen
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Abstract

We consider the isoperimetric problem with planar density equal to 1 on a horizontal strip and to a constant λ>1 outside the strip. We resolve a conjecture made by Cañete-Miranda Jr-Vittone by showing that every four-arc region admits a three-arc competitor with the same weighted area and strictly smaller weighted perimeter. The argument applies to every λ>1 and gives an explicit positive lower bound for the perimeter difference.

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Cite

BibTeXRIS
BibTeX
@misc{leon2026comparison,
  title = {{A comparison theorem for the planar strip isoperimetric problem}},
  author = {Skilyn Leon and Rosa Pavlak and Evelyn Pulla and Xi Sisi Shen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.36564},
  eprint = {2609.36564},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36564},
}
RIS
TY  - UNPB
TI  - A comparison theorem for the planar strip isoperimetric problem
AU  - Skilyn Leon
AU  - Rosa Pavlak
AU  - Evelyn Pulla
AU  - Xi Sisi Shen
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.36564
UR  - https://arxiv.org/abs/2609.36564
AB  - We consider the isoperimetric problem with planar density equal to 1 on a horizontal strip and to a constant λ>1 outside the strip. We resolve a conjecture made by Cañete-Miranda Jr-Vittone by showing that every four-arc region admits a three-arc competitor with the same weighted area and strictly smaller weighted perimeter. The argument applies to every λ>1 and gives an explicit positive lower bound for the perimeter difference.
ER  -