This course will focus on the analysis of the Laplacian and its resolvent, using techniques from `geometric microlocal analysis', on various classes of complete manifolds which exhibit different types of tame asymptotic structures (related to symmetric geometries) at infinity. Although there will be some discussion of the more familiar asymptotically Euclidean setting, the main emphasis will be on the class of asymptotically hyperbolic (conformally compact) manifolds, where there is a now extensively developed scattering theory. I will also treat some geometric applications, such as the theory of proper harmonic mappings between such spaces and of asymptotically hyperbolic Einstein metrics. In the latter part of the course, as time permits, I will discuss some new approaches to scattering on higher rank symmetric spaces of noncompact type (and perhaps some nonlinear problems in this context too).

This course will be an introduction to some modern techniques in linear PDE and geometric scattering theory, and most of the relevant analysis will be covered in full (or at least in detailed outline, with full references), assuming only a standard graduate-level course in elliptic PDE and some knowledge of distribution theory and Fourier analysis.

Zeit:       Mittwoch 10-12
Ort:        HG G 43 (Hermann-Weyl-Zimmer)
Beginn:   7. April
 

M. Struwe