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 , with special attention paid to corners. As an application, we solve the relative isoperimetric problem for a square with a square corner removed.
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!