Large riemannian

We study enhancement of diffusive mixing on a compact Riemannian manifold by a fast incompressible flow. Our main result is a sharp description of the class of flows that make the deviation of the solution from its average arbitrarily small in an arbitrarily short time, provided that the flow amplitude is large enough. The necessary and sufficient condition on such flows is expressed naturally in terms of the spectral properties of the dynamical system associated with the flow. In particular, we find that weakly mixing flows always enhance dissipation in this sense. ...

33p dontetvui 17-01-2013 51 10   Download

We study the large eigenvalue limit for the eigenfunctions of the Laplacian, on a compact manifold of negative curvature – in fact, we only assume that the geodesic flow has the Anosov property. In the semi-classical limit, we prove that the Wigner measures associated to eigenfunctions have positive metric entropy. In particular, they cannot concentrate entirely on closed geodesics. 1. Introduction, statement of results We consider a compact Riemannian manifold M of dimension d ≥ 2, and assume that the geodesic flow (g t )t∈R , acting on the unit tangent bundle of M , has a “chaotic”...

43p dontetvui 17-01-2013 55 8   Download

There are very few examples of Riemannian manifolds with positive sectional curvature known. In fact in dimensions above 24 all known examples are diffeomorphic to locally rank one symmetric spaces. We give a partial explanation of this phenomenon by showing that a positively curved, simply connected, compact manifold (M, g) is up to homotopy given by a rank one symmetric space, provided that its isometry group Iso(M, g) is large. More precisely we prove first that if dim(Iso(M, g)) ≥ 2 dim(M ) − 6, then M is tangentially homotopically equivalent to a rank one symmetric space or M...

63p noel_noel 17-01-2013 56 5   Download

For each k ∈ Z, we construct a uniformly contractible metric on Euclidean space which is not mod k hypereuclidean. We also construct a pair of uniformly contractible Riemannian metrics on Rn , n ≥ 11, so that the resulting manifolds Z and Z are bounded homotopy equivalent by a homotopy equivalence which is not boundedly close to a homeomorphism. We show that for these lf spaces the C ∗ -algebra assembly map K∗ (Z) → K∗ (C ∗ (Z)) from locally finite K-homology to the K-theory of the bounded propagation algebra is not a monomorphism ...

21p tuanloccuoi 04-01-2013 39 6   Download