Geometry and analysis of groups and manifolds

Geometric and analytic structures on metric spaces homeomorphic to a manifold

speaker: Stefan Wenger (University of Fribourg)

abstract: We explore geometric and analytic aspects of metric spaces homeomorphic to a closed, oriented manifold. We show that such spaces (which are sometimes called metric manifolds) admit a non-trivial integral current without boundary, provided they satisfy some weak assumptions. The existence of such an object should be thought of as an analytic analog of the fundamental class of the space and can also be interpreted as giving a way to make sense of Stokes' theorem in this setting. We use this to establish (relative) isoperimetric inequalities in metric n-manifolds that are Ahlfors n-regular and linearly locally contractible. As an application, we obtain a short and conceptually simple proof of a deep theorem of Semmes about the validity of Poincaré inequalities in these spaces. We furthermore present applications to the problem of Lipschitz-volume rigidity in the case of metric manifolds. Based on joint work with G. Basso and D. Marti.

timetable:
Thu 29 Jun, 9:00 - 10:00, Aula Dini
<< Go back