5 papers
Growth rates of Laplace eigenfunctions on the unit disk
Guillaume Lavoie, Guillaume Poliquin
We give a description of the growth rates of -normalized Laplace eigenfunctions on the unit disk with Dirichlet and Neumann boundary conditions. In particular, we show that th…
Principal frequency of the -Laplacian and the inradius of Euclidean domains
Guillaume Poliquin
We study the lower bounds for the principal frequency of the -Laplacian on -dimensional Euclidean domains. For , we obtain a lower bound for the first eigenvalue of the…
Superlevel sets and nodal extrema of Laplace-Beltrami eigenfunctions
Guillaume Poliquin
We estimate the volume of superlevel sets of Laplace-Beltrami eigenfunctions on a compact Riemannian manifold. The proof uses the Green's function representation and the Bathtub pr…
Bounds on the Principal Frequency of the -Laplacian
Guillaume Poliquin
This paper is concerned with the lower bounds for the principal frequency of the -Laplacian on -dimensional Euclidean domains. In particular, we extend the classical results…
Wolf-Keller theorem for Neumann eigenvalues
Guillaume Poliquin, Guillaume Roy-Fortin
The classical Szego-Weinberger inequality states that among bounded planar domains of given area, the first nonzero Neumann eigenvalue is maximized by a disk. Recently, it was show…