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Displaying 21 – 32 of 32

On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space.

Robert C. Reilly (1977)

Commentarii mathematici Helvetici

On the generic spectrum of a riemannian cover

Steven Zelditch (1990)

Annales de l'institut Fourier

Let $M$ be a compact manifold let $G$ be a finite group acting freely on $M$ , and let $ℳ_{G}$ be the (Fréchet) space of $G$ -invariant metric on $M$ . A natural conjecture is that, for a generic metric in $ℳ_{G}$ , all eigenspaces of the Laplacian are irreducible (as orthogonal representations of $G$ ). In physics terminology, no “accidental degeneracies” occur generically. We will prove this conjecture when dim $M \geq$ dim $V$ for all irreducibles $V$ of $G$ . As an application, we construct isospectral manifolds with simple eigenvalue...

On the multiplicity of eigenvalues of conformally covariant operators

Yaiza Canzani (2014)

Annales de l’institut Fourier

Let $(M, g)$ be a compact Riemannian manifold and $P_{g}$ an elliptic, formally self-adjoint, conformally covariant operator of order $m$ acting on smooth sections of a bundle over $M$ . We prove that if $P_{g}$ has no rigid eigenspaces (see Definition 2.2), the set of functions $f \in C^{\infty} (M, ℝ)$ for which $P_{e^{f} g}$ has only simple non-zero eigenvalues is a residual set in $C^{\infty} (M, ℝ)$ . As a consequence we prove that if $P_{g}$ has no rigid eigenspaces for a dense set of metrics, then all non-zero eigenvalues are simple for a residual set of metrics in the $C^{\infty}$ -topology....

On the Sobolev constant and the $p$ -spectrum of a compact riemannian manifold

Peter Li (1980)

Annales scientifiques de l'École Normale Supérieure

On the spectral theory and dynamics of asymptotically hyperbolic manifolds

Julie Rowlett (2010)

Annales de l’institut Fourier

We present a brief survey of the spectral theory and dynamics of infinite volume asymptotically hyperbolic manifolds. Beginning with their geometry and examples, we proceed to their spectral and scattering theories, dynamics, and the physical description of their quantum and classical mechanics. We conclude with a discussion of recent results, ideas, and conjectures.

On the spectral theory of the laplacian on noncompact hyperbolic manifolds

Shmuel Agmon (1987)

Journées équations aux dérivées partielles

On the Spectrum of Non-Compact Manifolds with Finite Volume.

Robert Brooks (1984)

Mathematische Zeitschrift

On the spectrum of Riemannian submersions with totally geodesic fibers

Gérard Besson, Manlio Bordoni (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this Note we give a rule to compute explicitely the spectrum and the eigenfunctions of the total space of a Riemannian submersion with totally geodesic fibers, in terms of the spectra and eigenfunctions of the typical fiber and any associated principal bundle.

Displaying 21 – 32 of 32

On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space.

On the generic spectrum of a riemannian cover

On the multiplicity of eigenvalues of conformally covariant operators

On the Sobolev constant and the $p$ -spectrum of a compact riemannian manifold

On the spectral theory and dynamics of asymptotically hyperbolic manifolds

On the spectral theory of the laplacian on noncompact hyperbolic manifolds

On the Spectrum of Non-Compact Manifolds with Finite Volume.

On the spectrum of Riemannian submersions with totally geodesic fibers

On the Wave Equation Asymptotics of a Compact Negatively Curved Surface.

On zeta function and scattering poles for several convex bodies

Opérateurs à bicaractéristiques périodiques

Operators on eigenmaps between spheres

Currently displaying 21 – 32 of 32