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arXiv · 2601.16285

Monotonicity of the first Dirichlet eigenvalue of regular polygons

Joel Dahne·Javier Gómez-Serrano·Joana Pech-Alberich
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Abstract

In this paper we prove that the first Dirichlet eigenvalue $\lambda_1^N$ of an $N$-sided regular polygon of fixed area is a monotonically decreasing function of $N$ for all $N \geq 3$, as well as the monotonicity of the quotients $\displaystyle \frac{\lambda_1^{N}}{\lambda_1^{N+1}}$. This settles a conjecture of Antunes-Freitas from 2006 [P. Antunes, P. Freitas, Experiment. Math., 15(3):333-342, 2006].

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Joel Dahne, Javier Gómez-Serrano, Joana Pech-Alberich. 2026-01-22. Monotonicity of the first Dirichlet eigenvalue of regular polygons. https://arxiv.org/abs/2601.16285

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