A Sharp Bound for the Ratio of the First Two Eigenvalues of Dirichlet Laplacians and Extensions

article by Mark S. Ashbaugh & Rafael Benguria published May 1992 in Annals of Mathematics

A Survey on the Krein–von Neumann Extension, the Corresponding Abstract Buckling Problem, and Weyl-type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

A second proof of the Payne-Pólya-Weinberger conjecture

article by Mark S. Ashbaugh & Rafael Benguria published June 1992 in Communications in Mathematical Physics

Best Constant for the Ratio of the First Two Eigenvalues of One-Dimensional Schrodinger Operators with Positive Potentials

Best constant for the ratio of the first two eigenvalues of one-dimensional Schrödinger operators with positive potentials

Book Review: Introduction to mechanics and symmetry: A basic exposition of classical mechanical systems

article published in 1996

Bounds for Ratios of Eigenvalues of the Dirichlet Laplacian

Bounds for ratios of eigenvalues of the Dirichlet Laplacian

Isoperimetric bound for $\lambda_3 / \lambda_2$ for the membrane problem

article by Mark S. Ashbaugh & Rafael Benguria published July 1991 in Duke Mathematical Journal

Isoperimetric bounds for higher eigenvalue ratios for the n-dimensional fixed membrane problem

Isoperimetric inequalities for eigenvalues of the Laplacian

Log-concavity of the ground state of Schrödinger operators: A new proof of the Baumgartner-Grosse-Martin inequality

article published in 1988

Low Eigenvalues of Laplace and Schrödinger Operators

More Bounds on Eigenvalue Ratios for Dirichlet Laplacians inNDimensions

On the Payne-Pólya-Weinberger conjecture on the n-dimensional sphere

On the ratio of the first two eigenvalues of Schrödinger operators with positive potentials

Optimal Lower Bound for the Gap Between the First Two Eigenvalues of One-Dimensional Schrodinger Operators with Symmetric Single-Well Potentials

Optimal bounds for ratios of eigenvalues of one-dimensional Schr�dinger operators with Dirichlet boundary conditions and positive potentials

Optimal lower bound for the gap between the first two eigenvalues of one-dimensional Schrödinger operators with symmetric single-well potentials

Proof of the Payne-Pólya-Weinberger conjecture

Sharp Upper Bound to the First Nonzero Neumann Eigenvalue for Bounded Domains in Spaces of Constant Curvature

article by Mark S. Ashbaugh & Rafael Benguria published October 1995 in Journal of the London Mathematical Society

Some eigenvalue inequalities for a class of Jacobi matrices

Some eigenvalue inequalities for a class of Jacobi matrices

Spectral theory for perturbed Krein Laplacians in nonsmooth domains

The Krein-von Neumann extension and its connection to an abstract buckling problem

The Range of Values of λ2/λ1 and λ3/λ1 for the Fixed Membrane Problem

The twisting tennis racket

Thomas-Fermi-von Weizs�cker equation

Universal Bounds for the Low Eigenvalues of Neumann Laplacians inNDimensions

generalization to three dimensions