Revista Matemática Iberoamericana
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Published online: 2018-08-27
Characterising Sobolev inequalities by controlled coarse homology and applications for hyperbolic spacesJuhani Koivisto (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. Iberoam. 34 (2018), 1055-1070. doi: 10.4171/RMI/1015