# Abstracts

Prof. Bernd Ammann und Mitarbeiter, Zimmer 119

## Construction of canonical, asymptotically Euclidean coordinates

In mathematical general relativity, one often assumes that the space-time is
foliated by space-like hypersurfaces such that each of these surfaces satisfies
certain asymptotic assumptions. The latter are often defined using coordinates.
For example, isolated gravitational systems are modeled by space-times which
are foliated by 'asymptotically Euclidean manifolds', i. e. it is assumed that
each leaf M possesses a coordinate system x mapping M (outside some compact
set) to the Euclidean space (outside some ball). This means that a physical
property is modeled using a non-geometric property which seems to be
counterintuitive. We will resolve this by constructing 'geometric coordinate
systems' using 'geometric spheres'. In this talk, we explain this for
asymptotically Euclidean and spheres of constant mean curvature (CMC).

Bernd Ammann, 11.12.2015 oder später