43 citations · 106 across the 34 of their papers we have counts for
47 papers
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…
The Golden Angle is not Constructible
Pedro J. Freitas
We prove that the golden angle (an angle that divides the circle in the golden ratio) is not constructible using straightedge and compass.