JournalsjstVol. 12, No. 2pp. 515–533

A proof of the triangular Ashbaugh–Benguria–Payne–Pólya–Weinberger inequality

  • Ryan Arbon

    UCLA, Los Angeles, USA

  • Mohammed Mannan

    New York University, USA

  • Michael Psenka

    UC Berkeley, USA

  • Seyoon Ragavan

    Princeton University, USA
A proof of the triangular Ashbaugh–Benguria–Payne–Pólya–Weinberger inequality cover
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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 (2010), who proved the inequality in the case of acute triangles. The proof utilizes inequalities due to Siudeja and Freitas (2010), together with improved variational bounds.

Cite this article

Ryan Arbon, Mohammed Mannan, Michael Psenka, Seyoon Ragavan, A proof of the triangular Ashbaugh–Benguria–Payne–Pólya–Weinberger inequality. J. Spectr. Theory 12 (2022), no. 2, pp. 515–533

DOI 10.4171/JST/409