Wave Asymptotics for Waveguides and Manifolds with Infinite Cylindrical Ends

Three-Manifolds and Manifolds with Cylindrical Ends

Contents Introduction. 1 Chapter 1. Four-dimensional Theory. 4 1. Setup. 4 2. A slice theorem for singular connections. 9 3. Laplacians on forms. 17 Chapter 2. Three-dimensional Theory. 22 1. Setup. 22 2. The Chern-Simons functional. 24 3. The deformation complex. 27 Chapter 3. Singular connections on manifolds with cylindrical ends. 33 1. Setup. 33 2. The translation-invariant case. 35 3. Glob...

Some Upper Bounds on the Number of Resonances for Manifolds with Infinite Cylindrical Ends

We prove some sharp upper bounds on the number of resonances associated with the Laplacian, or Laplacian plus potential, on a manifold with infinite cylidrical ends. The purpose of this note is to bound the number of resonances, poles of the meromorphic continuation of the resolvent, associated to a manifold with infinite cylindrical ends. These manifolds have an infinity which is in some sense...

Lefschetz Fixed Point Formula for Manifolds with Cylindrical Ends

Resonance asymptotics for asymptotically hyperbolic manifolds with warped-product ends

Resonance asymptotics for asymptotically hyperbolic manifolds with warped-product ends By Pascal Philipp We study the spectral theory of asymptotically hyperbolic manifolds with ends of warped-product type. Our main result is an upper bound on the resonance counting function, with a geometric constant expressed in terms of the respective Weyl constants for the core of the manifold and the base ...

Forward and Inverse Scattering on Manifolds with Asymptotically Cylindrical Ends

We study an inverse problem for a non-compact Riemannian manifold whose ends have the following properties : On each end, the Riemannian metric is assumed to be a short-range perturbation of the metric of the form (dy) + h(x, dx), h(x, dx) being the metric of some compact manifold of codimension 1. Moreover one end is exactly cylindrical, i.e. the metric is equal to (dy) +h(x, dx). Given two su...