Characterising Sobolev inequalities by controlled coarse homology and applications for hyperbolic spaces (Q1989537)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Characterising Sobolev inequalities by controlled coarse homology and applications for hyperbolic spaces |
scientific article |
Statements
Characterising Sobolev inequalities by controlled coarse homology and applications for hyperbolic spaces (English)
0 references
26 October 2018
0 references
The main result of the present paper establishes a Sobolev inequality characterisation for the vanishing of a fundamental class in the controlled coarse homology of Nowak-Špakula. The abstract setting corresponds to quasiconvex uniform spaces that support a local weak \((1,1)\)-Poincaré inequality. This result is applied in the framework of visual Gromov hyperbolic spaces and Carnot groups.
0 references
controlled coarse homology
0 references
Sobolev inequalities
0 references
