5 papers · 1 filter
An indefinite Coulomb interaction from the Steklov spectrum of perforated manifolds
Zhonggan Huang, Raghavendra Venkatraman
We establish optimal convergence rates for Steklov eigenvalues and harmonically extended eigenfunctions toward their weighted Laplace--Beltrami counterparts on a closed manifold pe…
Analytic spectral perturbation theory for a high-contrast Maxwell operator
Robert V. Kohn, Raghavendra Venkatraman
We study analytic spectral perturbation theory for the time-harmonic Maxwell operator in a perfectly electrically conducting cavity containing a high-contrast core--shell structure…
Transverse Magnetic ENZ Resonators: Robustness and Optimal Shape Design
Robert V. Kohn, Raghavendra Venkatraman
We study certain "geometric-invariant resonant cavitie"' introduced by Liberal et. al in a 2016 Nature Comm. paper, modeled using the transverse magnetic reduction of Maxwell's equ…
Optimal convergence rates for the spectrum of the graph Laplacian on Poisson point clouds
Scott Armstrong, Raghavendra Venkatraman
We prove optimal convergence rates for eigenvalues and eigenvectors of the graph Laplacian on Poisson point clouds. Our results are valid down to the critical percolation threshold…
Dirichlet eigenfunctions with nonzero mean value
Stefan Steinerberger, Raghavendra Venkatraman
We consider Laplacian eigenfunctions on a domain . Under Neumann boundary conditions, the first eigenfunction is constant and the others have mean value 0. T…