The Laplace operator on hyperbolic three manifolds with cusps of non-maximal rank.
The Laplace-Beltrami operator in almost-Riemannian Geometry
We study the Laplace-Beltrami operator of generalized Riemannian structures on orientable surfaces for which a local orthonormal frame is given by a pair of vector fields that can become collinear.Under the assumption that the structure is 2-step Lie bracket generating, we prove that the Laplace-Beltrami operator is essentially self-adjoint and has discrete spectrum. As a consequence, a quantum particle cannot cross the singular set (i.e., the set where the vector fields become collinear) and the...
The laplacian on asymptotically flat manifolds and the specification of scalar curvature
The large sieve in Riemann surfaces
The Leray measure of nodal sets for random eigenfunctions on the torus
We study nodal sets for typical eigenfunctions of the Laplacian on the standard torus in dimensions. Making use of the multiplicities in the spectrum of the Laplacian, we put a Gaussian measure on the eigenspaces and use it to average over the eigenspace. We consider a sequence of eigenvalues with growing multiplicity .The quantity that we study is the Leray, or microcanonical, measure of the nodal set. We show that the expected value of the Leray measure of an eigenfunction is constant, equal...
The Logarithmic Hardy-Littlewood-Sobolev Inequlity and Extremals of Zeta Functions on Sn.
The lower bound of the Ricci curvature that yields an infinite discrete spectrum of the Laplacian
This paper discusses the question whether the discrete spectrum of the Laplace-Beltrami operator is infinite or finite. The borderline-behavior of the curvatures for this problem will be completely determined.
The marked length spectrum vs. the Laplace spectrum on forms on Riemannian nilmanifolds.
The p-spectrum of the Laplacian on compact hyperbolic three manifolds.
The Quantum Birkhoff Normal Form and Spectral Asymptotics
In this talk we explain a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate potential well, yielding uniform estimates in the energy . This permits a detailed study of the spectrum in various asymptotic regions of the parameters , and gives improvements and new proofs for many of the results in the field. In the completely resonant...
The radiation field is a Fourier integral operator
We show that the ``radiation field'' introduced by F.G. Friedlander, mapping Cauchy data for the wave equation to the rescaled asymptotic behavior of the wave, is a Fourier integral operator on any non-trapping asymptotically hyperbolic or asymptotically conic manifold. The underlying canonical relation is associated to a ``sojourn time'' or ``Busemann function'' for geodesics. As a consequence we obtain some information about the high frequency behavior of the scattering...
The Residue of the Local Eta Function at the Origin.
The Scalar Curvature and the Spectrum of the Laplacian of Spin Manifolds.
The semiring of immersions of manifolds.
The spectra and the symmetric structure on a compact symmetric space.
The Spectrum of Fermat Curves.
The spectrum of the -Laplacian on Kähler manifolds
The spectrum of the Laplace operator for a spherical space form
Si determina lo spettro di un operatore di Laplace di una «spherical space form» e si studia l’influenza di tale spettro su .
The spectrum of the Laplace operator on conformally flat manifolds
The spectrum of the Laplacian on the warped products of Riemannian manifolds.