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arXiv · 2505.03047

The p-widths of a polygon

Otis Chodosh·Sithipont Cholsaipant
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Abstract

The $p$-widths are a nonlinear analogue of the spectrum of the Laplacian. We prove that each $p$-width of a polygon in $\mathbb{R}^2$ is achieved by a union of billiard trajectories. We also compute the $p$-widths of the equilateral triangle for $p=1,\dots,4$ and square for $p=1,\dots,3$.

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Otis Chodosh, Sithipont Cholsaipant. 2025-05-05. The p-widths of a polygon. https://arxiv.org/abs/2505.03047

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