Characterising Sobolev inequalities by controlled coarse homology and applications for hyperbolic spaces
Metric Geometry
2016-04-12 v5
Abstract
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 -Poincar\'e inequality. As applications, we consider visual Gromov hyperbolic spaces and Carnot groups.
Keywords
Cite
@article{arxiv.1402.5816,
title = {Characterising Sobolev inequalities by controlled coarse homology and applications for hyperbolic spaces},
author = {Juhani Koivisto},
journal= {arXiv preprint arXiv:1402.5816},
year = {2016}
}
Comments
Version for thesis including pre-examiner's suggestions