Estimates for sums of eigenvalues of the free plate with nonzero Poisson's ratio

An isoperimetric inequality for fundamental tones of free plates with nonzero Poisson's ratio

We establish a partial generalization of a prior isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate to plates of nonzero Poisson's ratio.

受拉自由圆板的振动模态

Vibrational modes of circular free plates under tension

受拉板的振动频率由方程$Δ^2u-τΔu=ωu$的本征值$ω$给出。本文确定了球上双拉普拉斯问题在自然（自由）边界条件下的本征函数和本征值。特别是，基本模式-最低的非零本征值的本征函数-被确定，并发现有简单的角度依赖性。

Ashbaugh–Benguria 关于Neumann特征值倒数和的猜想的一个证明

A proof of the Ashbaugh--Benguria conjecture for reciprocal sums of Neumann eigenvalues

证明了在固定体积的光滑有界区域中，球体最小化前m个非零Neumann特征值的倒数和，解决了Ashbaugh–Benguria猜想。