21 citations · 78 across the 17 of their papers we have counts for
15 papers · 1 filter
Isospectral CR manifolds with respect to the Kohn Laplacian
Gerson Gutierrez, Emilio A. Lauret, Juan Pablo Rossetti
We prove that the spectrum of the Kohn Laplacian does not determine the equivalence classes of CR manifolds. We construct pairs of odd-dimensional elliptic manifolds that are not e…
Do the Hodge spectra distinguish orbifolds from manifolds? Part 2
Katie Gittins, Carolyn Gordon, Ingrid Membrillo Solis +3
In \cite{GGKM-SSS} we examined the relationship between the singular set of a compact Riemannian orbifold and the spectrum of the Hodge Laplacian on -forms by computing the heat…
Recent results on the spectra of lens spaces
Emilio A. Lauret, Roberto J. Miatello, Juan Pablo Rossetti
In this paper we report on recent results by several authors, on the spectral theory of lens spaces and orbifolds and similar locally symmetric spaces of rank one. Most of these re…
Non-strongly isospectral spherical space forms
Emilio A. Lauret, Roberto J. Miatello, Juan Pablo Rossetti
In this paper we describe recent results on explicit construction of lens spaces that are not strongly isospectral, yet they are isospectral on -forms for every . Such exampl…
Spectra of lens spaces from 1-norm spectra of congruence lattices
Emilio A. Lauret, Roberto J. Miatello, Juan Pablo Rossetti
To every -dimensional lens space , we associate a congruence lattice in , with and we prove a formula relating the multiplicities of Hodge-…
Laplace-isospectral hyperbolic 2-orbifolds are representation-equivalent
Peter G. Doyle, Juan Pablo Rossetti
Using the Selberg trace formula, we show that for a hyperbolic 2-orbifold, the spectrum of the Laplacian acting on functions determines, and is determined by, the following data: t…
Strongly isospectral manifolds with nonisomorphic cohomology rings
Emilio A. Lauret, Roberto J. Miatello, Juan Pablo Rossetti
For any , , we give pairs of compact flat -manifolds with holonomy groups , that are strongly isospectral, hence isospectral on -form…
Isospectral orbifolds with different maximal isotropy orders
Juan Pablo Rossetti, Dorothee Schueth, Martin Weilandt
We construct pairs of compact Riemannian orbifolds which are isospectral for the Laplace operator on functions such that the maximal isotropy order of singular points in one of the…
Isospectral hyperbolic surfaces have matching geodesics
Peter G. Doyle, Juan Pablo Rossetti
We show that if two closed hyperbolic surfaces (not necessarily orientable or even connected) have the same Laplace spectrum, then for every length they have the same number of ori…
(Z_2^k)-manifolds are isospectral on forms
R. J. Miatello, R. A. Podesta, J. P. Rossetti
We obtain a simple formula for the multiplicity of eigenvalues of the Hodge-Laplace operator, , acting on sections of the full exterior bundle over an arbitrary compact flat R…
Tetra and Didi, the cosmic spectral twins
Peter G Doyle, Juan Pablo Rossetti
We introduce a pair of isospectral but non-isometric compact flat 3-manifolds called Tetra (a tetracosm) and Didi (a didicosm). The closed geodesics of Tetra and Didi are very diff…
Hearing the platycosms
J. P. Rossetti, J. H. Conway
A `platycosm' is a flat Riemannian 3-manifold without boundary. In this paper we prove that there is (up to scale) a unique isospectral pair of compact platycosms.
Flat Manifolds Isospectral on p-Forms
R. J. Miatello, J. P. Rossetti
We study isospectrality on p-forms of compact flat manifolds by using the equivariant spectrum of the Hodge-Laplacian on the torus. We give an explicit formula for the multiplicity…
Boundary volume and length spectra of Riemannian manifolds: What the middle degree Hodge spectrum doesn't reveal
Carolyn S. Gordon, J. P. Rossetti
Let be a -dimensional compact Riemannian manifold. We show that the spectrum of the Hodge Laplacian acting on -forms does not determine whether the manifold has boundary…
Length spectra and p-spectra of compact flat manifolds
R. J. Miatello, J. P. Rossetti
We study the length, weak length and complex length spectrum of closed geodesics of a compact flat Riemannian manifold, comparing length-isospectrality with isospectrality of the L…