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Boundary volume and length spectra of Riemannian manifolds: what the middle degree Hodge spectrum doesn't reveal

Carolyn S. Gordon, Juan Pablo Rossetti (2003)

Annales de l'Institut Fourier

Let M be a 2 m -dimensional compact Riemannian manifold. We show that the spectrum of the Hodge Laplacian acting on m -forms does not determine whether the manifold has boundary, nor does it determine the lengths of the closed geodesics. Among the many examples are a projective space and a hemisphere that have the same Hodge spectrum on 1- forms, and hyperbolic surfaces, mutually isospectral on 1-forms, with different injectivity radii. The Hodge m -spectrum also does not distinguish orbifolds from manifolds....

Bounded almost global solutions for non hamiltonian semi-linear Klein-Gordon equations with radial data on compact revolution hypersurfaces

Jean-Marc Delort, Jérémie Szeftel (2006)

Annales de l’institut Fourier

This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on compact revolution hypersurfaces with non-Hamiltonian nonlinearities, when the data are smooth, small and radial. The method combines normal forms with the fact that the eigenvalues associated to radial eigenfunctions of the Laplacian on such manifolds are simple and satisfy convenient asymptotic expansions.

Bounded cohomology and isometry groups of hyperbolic spaces

Ursula Hamenstädt (2008)

Journal of the European Mathematical Society

Let X be an arbitrary hyperbolic geodesic metric space and let Γ be a countable subgroup of the isometry group Iso ( X ) of X . We show that if Γ is non-elementary and weakly acylindrical (this is a weak properness condition) then the second bounded cohomology groups H b 2 ( Γ , ℝ ) , H b 2 ( Γ , ℓ p ( Γ ) ) ( 1 < ...

Bounding the degree of solutions to Pfaff equations

Marco Brunella, Luis Gustavo Mendes (2000)

Publicacions Matemàtiques

We study hypersurfaces of complex projective manifolds which are invariant by a foliation, or more generally which are solutions to a Pfaff equation. We bound their degree using classical results on logarithmic forms.

Brownian motion and random walks on manifolds

Nicolas Th. Varopoulos (1984)

Annales de l'institut Fourier

We develop a procedure that allows us to “descretise” the Brownian motion on a Riemannian manifold. We construct thus a random walk that is a good approximation of the Brownian motion.

Brownian motion and transient groups

Nicolas Th. Varopoulos (1983)

Annales de l'institut Fourier

In this paper I consider M ˜ → M a covering of a Riemannian manifold M . I prove that Green’s function exists on M ˜ if any and only if the symmetric translation invariant random walks on the covering group G are transient (under the assumption that M is compact).

Currently displaying 61 – 80 of 88