43 citations · 106 across the 34 of their papers we have counts for
22 papers · 1 filter
Spherical n-lunes: billiards and eigenvalues
Pedro Freitas, Isabel Salavessa
We characterise the periodic orbits of geodesic billiards on spherical lunes on . In the case of angle openings of the form for positive integer we fully…
Recurrence formulae for spectral determinants
J. Cunha, P. Freitas
We develop a unified method to study spectral determinants for several different manifolds, including spheres and hemispheres, and projective spaces. This is a direct consequence o…
On domain monotonicity of Neumann eigenvalues of convex domains
Pedro Freitas, James B. Kennedy
Inspired by a recent result of Funano's, we provide a sharp quantitative comparison result between the first nontrivial eigenvalues of the Neumann Laplacian on bounded convex domai…
Families of non-tiling domains satisfying Pólya's conjecture
Pedro Freitas, Isabel Salavessa
We show the existence of classes of non-tiling domains satisfying Pólya's conjecture in any dimension, in both the Euclidean and non-Euclidean cases. This is a consequence of a mor…
Pólya-type inequalities on spheres and hemispheres
Pedro Freitas, Jing Mao, Isabel Salavessa
Given an eigenvalue of the Laplace-Beltrami operator on spheres or hemispheres, with multiplicity such that , we characterise the lowest a…
Two balls maximize the third Neumann eigenvalue in hyperbolic space
Pedro Freitas, Richard S. Laugesen
We show that the third eigenvalue of the Neumann Laplacian in hyperbolic space is maximal for the disjoint union of two geodesic balls, among domains of given volume. This extends…