The p-widths of a polygon

Otis Chodosh; Sithipont Cholsaipant

The p-widths of a polygon

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arxiv 2505.03047 v1 pith:PQ7BSFTL submitted 2025-05-05 math.DG

Otis Chodosh , Sithipont Cholsaipant This is my paper

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keywords dotspolygonwidthsachievedanaloguebilliardcomputeequilateral

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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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