7 papers
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…
Convergence of Empirical Measures for i.i.d. samples in
Gautam Iyer, Raghavendra Venkatraman
Given i.i.d. samples from a probability measure on , we study the rate of convergence of the empirical measure in the negative Sobolev space $W…
Quantitative homogenization and large-scale regularity of Poisson point clouds
Scott Armstrong, Raghavendra Venkatraman
We prove quantitative homogenization results for harmonic functions on supercritical continuum percolation clusters--that is, Poisson point clouds with edges connecting points whic…
Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds
Nicolás GarcÃa Trillos, Chenghui Li, Raghavendra Venkatraman
We study the problem of estimating eigenpairs of elliptic differential operators from samples of a distribution supported on a manifold . The operators discussed in the pap…
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.…