Suppose that (X, g) is a conformally compact (n+1)-dimensional manifold that is hyperbolic near infinity in the sense that the sectional curvatures of g are identically equal to minus one outside of a compact set K ⊂ X. We prove that the counting function for the resolvent resonances has maximal order of growth (n + 1) generically for such manifolds. This is achieved by constructing explicit ex...

The Palais-Smale Condition C holds for the Yang-Mills functional on principal bundles over compact manifolds of dimension ≤ 3. This was established by S. Sedlacek [17] and C. Taubes [18] Proposition 4.5 using the compactness theorem of K. Uhlenbeck [20]; see also [23]. It is well known that Condition C fails for Yang-Mills over compact manifolds of dimension ≥ 4. The example of SO(3)-invariant ...

We define a regularized version of an equivariant index of a (generalized) Dirac operator on a non-compact complete Riemannian manifold M acted on by a compact Lie group G. Our definition requires an additional data – an equivariant map v : M → g = LieG, such that the corresponding vector field on M does not vanish outside of a compact subset. For the case when M = C and G is the circle group a...

In this short paper we show that non-negative Ricci curvature is not preserved under Ricci flow for closed manifolds of dimensions four and above, strengthening a previous result of Knopf for complete non-compact manifolds of bounded curvature. This brings down to four dimensions a similar result Böhm and Wilking have for dimensions twelve and above. Moreover, the manifolds constructed here are...

Stable ergodicity is dense among compact Lie group extensions of Anosov dif-feomorphisms of compact manifolds. Under the additional assumption that the base map acts on an infranilmanifold, an extension that is not stably ergodic must have a factor that has one of three special forms. A consequence is that stable ergodicity and stable ergodicity within skew products are equivalent in this case....

Let f be a bounded function on the real line IF!. One may characterize the structural properties off by the modulus of smoothness w(t,f) = sup{lf (4 -f( y)l; x, y E 08, I x y I < t>, and, if w(t) is a continuous nondecreasing function of t > 0 such that w(O) = 0, by the Lipschitz class Lip(w) which is the set of all continuous functions such that su~~<~<i w(t, f)/o(t) < 00. It is possible to ex...

The fundamental group of compact manifolds without conjugate points.

In this paper theorems are proved which provide for lifting and projecting expansive homeomorphisms through pseudocovering mappings so that the lift or projection is also an expansive homeomorphism. Using these techniques it is shown that the compact orientable surface of genus 2 admits an expansive homeomorphism.

Properties of Cantor manifolds that could arise in the quantum gravitational path integral are investigated. The spin geometry is compared to the intersection of Cantor sets. Given a network consisting of unions of Riemann surfaces in a superstring theory, the probable value of the number of dimensions is initially ten, and after compactification of six coordinates, the space-time would be expe...

We study Sobolev spaces on Lie manifolds, which we define as a class of manifolds described by vector fields (see Definition 1.2). The class of Lie manifolds includes the Euclidean spaces Rn, asymptotically flat manifolds, conformally compact manifolds, and manifolds with cylindrical and polycylindrical ends. As in the classical case of Rn, we define Sobolev spaces using derivatives, powers of ...