Revista Matemática Iberoamericana


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Volume 34, Issue 3, 2018, pp. 1055–1070
DOI: 10.4171/RMI/1015

Published online: 2018-08-27

Characterising Sobolev inequalities by controlled coarse homology and applications for hyperbolic spaces

Juhani Koivisto[1]

(1) University of Southern Denmark, Odense, Denmark

We give a Sobolev inequality characterisation for the vanishing of the fundamental class in the controlled coarse homology of Nowak and Špakula for quasiconvex uniform spaces that support a local weak (1, 1)-Poincaré inequality. Among the applications, we consider visual Gromov hyperbolic spaces.

Keywords: Controlled coarse homology, Sobolev inequalities

Koivisto Juhani: Characterising Sobolev inequalities by controlled coarse homology and applications for hyperbolic spaces. Rev. Mat. Iberoamericana 34 (2018), 1055-1070. doi: 10.4171/RMI/1015