27 citations · 142 across the 17 of their papers we have counts for
7 papers · 1 filter
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…
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…
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…
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…
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…
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…