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

2014/02/24 by Koivisto, Juhani
#30L99 #FOS: Mathematics #Metric Geometry (math.MG) #Primary 53C23 #Secondary 58J32

paper · doi:10.48550/arxiv.1402.5816

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 (1,1)-Poincaré inequality. As applications, we consider visual Gromov hyperbolic spaces and Carnot groups.

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