A Proof of The Triangular Ashbaugh-Benguria-Payne-P\'{o}lya-Weinberger Inequality
Spectral Theory
2022-11-10 v2
Abstract
In this paper, we show that for all triangles in the plane, the equilateral triangle maximizes the ratio of the first two Dirichlet-Laplacian eigenvalues. This is an extension of work by Siudeja, who proved the inequality in the case of acute triangles. The proof utilizes inequalities due to Siudeja and Freitas, together with improved variational bounds.
Keywords
Cite
@article{arxiv.2009.00927,
title = {A Proof of The Triangular Ashbaugh-Benguria-Payne-P\'{o}lya-Weinberger Inequality},
author = {Ryan Arbon and Mohammed Mannan and Michael Psenka and Seyoon Ragavan},
journal= {arXiv preprint arXiv:2009.00927},
year = {2022}
}
Comments
16 pages, 4 figures