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Radon transforms and spectral rigidity on the complex quadrics and the real Grassmannians of rank two.

H. Goldschmidt, J. Gasqui (1996)

Journal für die reine und angewandte Mathematik

Recovering quantum graphs from their Bloch spectrum

Ralf Rueckriemen (2013)

Annales de l’institut Fourier

We define the Bloch spectrum of a quantum graph to be the map that assigns to each element in the deRham cohomology the spectrum of an associated magnetic Schrödinger operator. We show that the Bloch spectrum determines the Albanese torus, the block structure and the planarity of the graph. It determines a geometric dual of a planar graph. This enables us to show that the Bloch spectrum indentifies and completely determines planar $3$ -connected quantum graphs.

Recursion relations and the asymptotic behavior of the eigenvalues of the laplacian

Peter B. Gilkey (1979)

Compositio Mathematica

Regularity properties of the generalized hamiltonian flow

L. Stoyanov (1992/1993)

Séminaire Équations aux dérivées partielles (Polytechnique)

Relation de Poisson pour l'équation des ondes dans un ouvert non borné. Application au scattering

Claude Bardos, Jean-Claude Guillot, James Ralston (1980)

Journées équations aux dérivées partielles

Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds

Svatopluk Krýsl (2007)

Archivum Mathematicum

Consider a flat symplectic manifold $(M^{2 l}, ω)$ , $l \geq 2$ , admitting a metaplectic structure. We prove that the symplectic twistor operator maps the eigenvectors of the symplectic Dirac operator, that are not symplectic Killing spinors, to the eigenvectors of the symplectic Rarita-Schwinger operator. If $λ$ is an eigenvalue of the symplectic Dirac operator such that $- ı l λ$ is not a symplectic Killing number, then $\frac{l - 1}{l} λ$ is an eigenvalue of the symplectic Rarita-Schwinger operator.

Remarque sur un article de Marcel Berger : «Sur une inégalité pour la première valeur propre du laplacien»

Pierre Bérard, Gérard Besson (1980)

Bulletin de la Société Mathématique de France

Remarques sur la conjecture de Weyl

Pierre H. Bérard (1983)

Compositio Mathematica

Representations of Compact Lie Groups and Elliptic Operators.

Ernst Heintze, Jochen Brüning (1978/1979)

Inventiones mathematicae

Représentations relativement équivalentes et variétés riemanniennes isospectrales.

Hubert Pesce (1996)

Commentarii mathematici Helvetici

Resolvent at low energy and Riesz transform for Schrödinger operators on asymptotically conic manifolds. II

Colin Guillarmou, Andrew Hassell (2009)

Annales de l’institut Fourier

Let $M^{\circ}$ be a complete noncompact manifold of dimension at least 3 and $g$ an asymptotically conic metric on $M^{\circ}$ , in the sense that $M^{\circ}$ compactifies to a manifold with boundary $M$ so that $g$ becomes a scattering metric on $M$ . We study the resolvent kernel ${(P + k^{2})}^{- 1}$ and Riesz transform $T$ of the operator $P = Δ_{g} + V$ , where $Δ_{g}$ is the positive Laplacian associated to $g$ and $V$ is a real potential function smooth on $M$ and vanishing at the boundary.In our first paper we assumed that $P$ has neither zero modes nor a zero-resonance and showed...

Résonances

Yves Colin de Verdière (1984/1985)

Séminaire de théorie spectrale et géométrie

Ricci curvature and qusiconformal deformations of a Riemannian manifold.

Antoni Pierzchalski (1990)

Manuscripta mathematica

Riemannian manifolds whose Laplacians have purely continuous spectrum.

Harold Donnelly, Nicola Garafalo (1992)

Mathematische Annalen

Riemannian manifolds with maximal eigenfunction growth

Christopher D. Sogge (2000/2001)

Séminaire Équations aux dérivées partielles

Riesz transform on manifolds and heat kernel regularity

Pascal Auscher, Thierry Coulhon, Xuan Thinh Duong, Steve Hofmann (2004)

Annales scientifiques de l'École Normale Supérieure

Rigidity and $L^{2}$ cohomology of hyperbolic manifolds

Gilles Carron (2010)

Annales de l’institut Fourier

When $X = Γ ∖ ℍ^{n}$ is a real hyperbolic manifold, it is already known that if the critical exponent is small enough then some cohomology spaces and some spaces of $L^{2}$ harmonic forms vanish. In this paper, we show rigidity results in the borderline case of these vanishing results.

Currently displaying 1 – 20 of 20

Page 1

Displaying 1 – 20 of 20

Radon transforms and spectral rigidity on the complex quadrics and the real Grassmannians of rank two.

Recovering quantum graphs from their Bloch spectrum

Recursion relations and the asymptotic behavior of the eigenvalues of the laplacian

Regularity properties of the generalized hamiltonian flow

Relation de Poisson pour l'équation des ondes dans un ouvert non borné. Application au scattering

Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds

Remarque sur un article de Marcel Berger : «Sur une inégalité pour la première valeur propre du laplacien»

Remarques sur la conjecture de Weyl

Representations of Compact Lie Groups and Elliptic Operators.

Représentations relativement équivalentes et variétés riemanniennes isospectrales.

Resolvent at low energy and Riesz transform for Schrödinger operators on asymptotically conic manifolds. II

Résonances

Ricci curvature and qusiconformal deformations of a Riemannian manifold.

Riemannian manifolds whose Laplacians have purely continuous spectrum.

Riemannian manifolds with maximal eigenfunction growth

Riesz transform on manifolds and heat kernel regularity

Rigidity and $L^{2}$ cohomology of hyperbolic manifolds

Rigidity of generalized laplacians and some geometric applications. (Summary).

Rigidity of generalized laplacians and some geometric applications.

R-torsion and zeta functions for locally symmetric manifolds.

Currently displaying 1 – 20 of 20