Patrick Foulon

Sur les variétés compactes asymptotiquement harmoniques

A pair of reed switches are magnetically actuated by a flow sensing spool in the hydraulic circuit.

Locally symmetric Finsler spaces in negative curvature

Abstract E. Cartan introduced in 1926 the Riemannian locally symmetric spaces, as the spaces whose curvature tensor is parallel. They also owe their name to the fact that, for each point, the geodesic reflexion is a local isometry. The aim of this Note is to announce a strong rigidity result for Finsler spaces. Namely, we show that a negatively curved locally symmetric (in the first sense above) Finsler space is isometric to a Riemann locally symmetric space.

Zygmund strong foliations

We show that for a volume-preserving Anosov flow on a 3-manifold the strong stable and unstable foliations are Zygmund-regular. We also exhibit an obstruction to higher regularity, which admits a direct geometric interpretation. Vanishing of this obstruction implies high smoothness of the joint strong subbundle and that the flow is either a suspension or a contact flow.