论文标题
三角形的Ashbaugh-Benguria-Payne-Payne-Payne-weinberger不平等的证明
A Proof of The Triangular Ashbaugh-Benguria-Payne-Pólya-Weinberger Inequality
论文作者
论文摘要
在本文中，我们表明，对于平面中的所有三角形，等边三角形最大化了前两个Dirichlet-Laplacian特征值的比率。这是Siudeja的工作延伸，他在急性三角形的情况下证明了不平等。该证明利用了由于Siudeja和Freitas而引起的不平等，以及改善的变化界限。
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.
