On Ashbaugh-Benguria's Conjecture about Lower Order Dirichlet Eigenvalues of the Laplacian. (arXiv:1810.09415v1 [math.AP])

In this paper, we prove an isoperimetric inequality for lower order eigenvalues of the Dirichlet Laplacian in bounded domains of a Euclidean space which strengthens the well-known Ashbaugh-Beguria inequality about the ratio of the first two Dirichlet eigenvalues of the same domains and supports strongly a conjecture of Ashbaugh-Benguria. 查看全文>>