Ball-Homogeneous and Disk-Homogeneous Riemannian Manifolds.
On montre l’équivalence entre l’hyperbolicité au sens de Gromov de la géométrie de Hilbert d’un domaine convexe du plan et la non nullité du bas du spectre de ce domaine.
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, 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 -spectrum also does not distinguish orbifolds from manifolds....