Characterising Sobolev inequalities by controlled coarse homology and   applications for hyperbolic spaces
  We give a Sobolev inequality characterisation for the vanishing of a fundamental class in the controlled coarse homology of Nowak and Spakula for quasiconvex uniform spaces that support a local weak $(1,1)$-Poincar\'e inequality. As applications, we consider visual Gromov hyperbolic spaces and Carnot groups. 
Juhani Koivisto
math.MG