29 citations · 192 across the 45 of their papers we have counts for
55 papers
Payne's conjecture for buckling eigenvalues of odd index
Michael Levitin, Iosif Polterovich
In 1955, L. E. Payne conjectured that for a planar clamped plate, each buckling eigenvalue is at least as large as the Dirichlet Laplacian eigenvalue of the same domain with index…
An isoperimetric problem for Fourier zeros of centrally symmetric convex bodies
Javier Gómez-Serrano, Michael Levitin, Daniel Platt +1
Given a centrally symmetric convex body, consider the zero set of the Fourier transform of its characteristic function. We study how large the distance from this set to the origin…
Comparison inequalities for Dirichlet-to-Neumann maps
Denis S. Grebenkov, Michael Levitin, Karl-Mikael Perfekt +1
We prove comparison inequalities for Dirichlet-to-Neumann maps corresponding to different non-positive Helmholtz parameters. For convex domains our bounds are sharp, and the result…
The Faber-Krahn position of convex bodies and Gaussian measure inequalities
Dmitry Faifman, Iosif Polterovich
We say that a convex body is in Faber-Krahn position if it minimizes the first Dirichlet eigenvalue within its volume-preserving linear orbit. We prove that this position is unique…
Pólya's conjecture for higher-dimensional Neumann balls
Nikolay Filonov, Michael Levitin, Iosif Polterovich +1
We prove Pólya's conjecture for the Neumann eigenvalues of the Laplacian on Euclidean balls in dimensions three and higher. The proof further develops the approach introduced in ou…
Spectral properties of the Dirichlet-to-Neumann map for the Helmholtz equation
Denis S. Grebenkov, Michael Levitin, Iosif Polterovich
The study of the Dirichlet-to-Neumann map and the associated Steklov problem for the Laplace equation has been a central topic in spectral geometry over the past decade. In this su…