English

Remarks on the relative isoperimetric profile of polygonal domains in $\mathbb{R}^2$

Differential Geometry 2026-05-25 v1

Abstract

We develop techniques for solving the relative isoperimetric problem on polygonal domains in R2\mathbb{R}^2, with special attention paid to corners. As an application, we solve the relative isoperimetric problem for a square with a square corner removed.

Keywords

Cite

@article{arxiv.2605.23149,
  title  = {Remarks on the relative isoperimetric profile of polygonal domains in $\mathbb{R}^2$},
  author = {Jason DeVito and Robert DeYeso and Ezra Nance and Robert Niedzialomski},
  journal= {arXiv preprint arXiv:2605.23149},
  year   = {2026}
}

Comments

24 pages and 14 figures. Comments welcome!