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arXiv · 2609.32946

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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Kyle Byassee, Hunter Johnson, Brandon Jones, Ezra Nance. 2026-09-26. The relative isoperimetric profile of a unit square with a central square removed. https://arxiv.org/abs/2609.32946

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