Global ultradifferentiable hypoellipticity on compact manifolds

On global hypoellipticity

We consider a first order linear partial differential operator of principal type on a closed connected orientable two-dimensional manifold sending sections of one complex line bundle to sections of another. We prove that the assumption of global hypoellipticity of the operator implies a relation between the degrees of the line bundles and the Euler characteristic of the manifold.

Surgery on Compact Manifolds

Lipschitz Spaces on Compact Manifolds

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...

Expansive Homeomorphisms on Compact Manifolds

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.

Continuous Wavelets on Compact Manifolds

Let M be a smooth compact oriented Riemannian manifold, and let ∆M be the Laplace-Beltrami operator on M. Say 0 6= f ∈ S(R), and that f(0) = 0. For t > 0, let Kt(x, y) denote the kernel of f(t∆M). We show that Kt is well-localized near the diagonal, in the sense that it satisfies estimates akin to those satisfied by the kernel of the convolution operator f(t∆) on R. We define continuous S-wavel...