Abstract:

In this talk I will illustrate how the use of quasi-isometry invariant functional spaces is useful in understanding the large scale geometry of negatively curved spaces. I will focus on the $L^p$ cohomology and its applications to homogeneous manifolds of negative curvature (Heintze groups). I will then consider a larger class of funtional spaces (Orlicz spaces) and generalize some of the results explained in the first part of the talk. I will motivate the notions and results of the talk by many examples.