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In this paper, we show that for all triangles in the plane, the equilateraltriangle maximizes the ratio of the first two Dirichlet-Laplacian eigenvalues.This is an extension of work by Siudeja, who proved the inequality in the caseof acute triangles. The proof utilizes inequalities due to Siudeja and Freitas,together with improved variational bounds.

A Proof of The Triangular Ashbaugh-Benguria-Payne-P\'{o}lya-Weinberger Inequality