EVENT DETAILS AND ABSTRACT

Title: The exponential map on singular spaces
Speaker: Daniel Grieser
Speaker Info: Oldenburg
Brief Description:
Special Note: Note unusual time
Abstract:

We study singular spaces embedded in a smooth Riemannian manifold, and in particular the geodesics running into, or close to, a singularity. Focussing on conical, cuspidal and mixed conic/cuspidal isolated singularities we first consider the question which classes of (degenerating) metrics arise on manifolds with boundary as resolutions of metrics on singular spaces. This can be formulated in terms of certain closedness and exactness conditions. We also identify essential invariants of these metrics. We then give a detailed description of the exponential map based at a singular point. While in the conical case this map behaves almost as in the smooth situation (as shown in work by Melrose and Wunsch), the cusp case yields an wide variety of non-standard possible behavior. An essential role is played by a damped Hamiltonian system on the boundary involving a potential which describes the cross section of the cusp singularity.