8 papers
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…
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 o…
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…
The exterior Steklov problem for Euclidean domains
Lukas Bundrock, Alexandre Girouard, Denis S. Grebenkov +2
We investigate the Steklov eigenvalue problem in an exterior Euclidean domain. First, we present several formulations of this problem and establish the equivalences between them. N…
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…
Pólya's conjecture for Dirichlet eigenvalues of annuli
Nikolay Filonov, Michael Levitin, Iosif Polterovich +1
We prove Pólya's conjecture for the eigenvalues of the Dirichlet Laplacian on annular domains. Our approach builds upon and extends the methods we previously developed for disks a…