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arXiv · 2605.23149

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

Jason DeVito·Robert DeYeso III·Ezra Nance·Robert Niedzialomski
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Abstract

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

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Jason DeVito, Robert DeYeso III, Ezra Nance, Robert Niedzialomski. 2026-05-22. Remarks on the relative isoperimetric profile of polygonal domains in $\mathbb{R}^2$. https://arxiv.org/abs/2605.23149

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