27 citations · 142 across the 17 of their papers we have counts for
20 papers
On Pleijel's nodal domain theorem for the Robin problem
Asma Hassannezhad, David Sher
We prove an improved Pleijel nodal domain theorem for the Robin eigenvalue problem. In particular we remove the restriction, imposed in previous work, that the Robin parameter be n…
Some recent developments on the Steklov eigenvalue problem
Bruno Colbois, Alexandre Girouard, Carolyn Gordon +1
The Steklov eigenvalue problem, first introduced over 125 years ago, has seen a surge of interest in the past few decades. This article is a tour of some of the recent developments…
Joint asymptotic expansions for Bessel functions
David A. Sher
We study the classical problem of finding asymptotics for the Bessel functions and as the argument and the order approach infinity. We use blow-up analysi…
Pólya's conjecture for Euclidean balls
Nikolay Filonov, Michael Levitin, Iosif Polterovich +1
The celebrated Pólya's conjecture (1954) in spectral geometry states that the eigenvalue counting functions of the Dirichlet and Neumann Laplacian on a bounded Euclidean domain can…
Nodal count for Dirichlet-to-Neumann operators with potential
Asma Hassannezhad, David Sher
We consider Dirichlet-to-Neumann operators associated to on a Lipschitz domain in a smooth manifold, where is an potential. We prove a Courant-type bound for…
How to hear the corners of a drum
Medet Nursultanov, Julie Rowlett, David Sher
We announce a new result which shows that under either Dirichlet, Neumann, or Robin boundary conditions, the corners in a planar domain are a spectral invariant of the Laplacian. F…
Inverse Steklov spectral problem for curvilinear polygons
Stanislav Krymski, Michael Levitin, Leonid Parnovski +2
This paper studies the inverse Steklov spectral problem for curvilinear polygons. For generic curvilinear polygons with angles less than , we prove that the asymptotics of Stekl…
The heat kernel on curvilinear polygonal domains in surfaces
Medet Nursultanov, Julie Rowlett, David A. Sher
We construct the heat kernel on curvilinear polygonal domains in arbitrary surfaces for Dirichlet, Neumann, and Robin boundary conditions as well as mixed problems, including those…
On the pseudospectra of Schrödinger operators on Zoll manifolds
David Sher, Alejandro Uribe, Carlos Villegas-Blas
We consider non-self-adjoint Schrödinger operators where is the Laplace-Beltrami operator on a Zoll manifold and . We obtain asymptotic re…
A Cheeger-Müller theorem for manifolds with wedge singularities
Pierre Albin, Frédéric Rochon, David Sher
We study the spectrum and heat kernel of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold degenerating to a manifold with wedge singularities. Provided t…
Sloshing, Steklov and corners: Asymptotics of sloshing eigenvalues
Michael Levitin, Leonid Parnovski, Iosif Polterovich +1
In the present paper we develop an approach to obtain sharp spectral asymptotics for Steklov type problems on planar domains with corners. Our main focus is on the two-dimensional…
Nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces
Iosif Polterovich, David A. Sher, John A. Toth
We prove sharp upper and lower bounds for the nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces with boundary. The argument involves frequency function me…
Analytic torsion and R-torsion of Witt representations on manifolds with cusps
Pierre Albin, Frédéric Rochon, David Sher
We establish a Cheeger-Muller theorem for unimodular representations satisfying a Witt condition on a noncompact manifold with cusps. This class of spaces includes all non-compact…
Resolvent, heat kernel and torsion under degeneration to fibered cusps
Pierre Albin, Frédéric Rochon, David Sher
Manifolds with fibered cusps are a class of complete noncompact Riemannian manifolds including all locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacia…
The Steklov spectrum of surfaces: asymptotics and invariants
Alexandre Girouard, Leonid Parnovski, Iosif Polterovich +1
We obtain precise asymptotics for the Steklov eigenvalues on a compact Riemannian surface with boundary. It is shown that the number of connected components of the boundary, as wel…
Low energy resolvent for the Hodge Laplacian: Applications to Riesz transform, Sobolev estimates and analytic torsion
Colin Guillarmou, David A. Sher
On an asymptotically conic manifold , we analyze the asymptotics of the integral kernel of the resolvent of the Hodge Laplacian on -forms a…
Heat invariants of the Steklov problem
Iosif Polterovich, David A. Sher
We study the heat trace asymptotics associated with the Steklov eigenvalue problem on a Riemannian manifold with boundary. In particular, we describe the structure of the Steklov h…
The determinant on flat conic surfaces with excision of disks
David A. Sher
Let M be a surface with conical singularities, and consider a degenerating family of surfaces obtained from M by removing disks of smaller and smaller radius around a subset of the…
Conic degeneration and the determinant of the Laplacian
David A. Sher
We investigate the behavior of various spectral invariants, particularly the determinant of the Laplacian, on a family of smooth Riemannian manifolds which undergo conic degenerati…
The heat kernel on an asymptotically conic manifold
David A. Sher
In this paper, we investigate the long-time structure of the heat kernel on a Riemannian manifold M which is asymptotically conic near infinity. Using geometric microlocal analysis…