Past lectures

Abstract

Building on some well known results for elliptic operators in bounded domains, we will cover the most important aspects of the analysis of elliptic operators on manifolds with cylindrical ends.

We will explain how these techniques can be used to understand the moduli space theory of some non-compact problems in geometry: minimal surfaces with catenoid ends, constant mean curvature surfaces with Delaunay ends, complete constant scalar curvature metrics with ends, ...

We will determine the formal dimension of the corresponding moduli spaces and we will also explain many connected sum results that provide the existence of these geometric objects.

Finally, we will also explain how to use these techniques in constructing solutions of singularly perturbed problems that arise in nonlinear analysis but also in geometry (extremal metrics in Kähler geometry).