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arXiv · 1402.5816

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

Juhani Koivisto
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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 $(1,1)$-Poincar\'e inequality. As applications, we consider visual Gromov hyperbolic spaces and Carnot groups.

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Juhani Koivisto. 2014-02-24. Characterising Sobolev inequalities by controlled coarse homology and applications for hyperbolic spaces. https://arxiv.org/abs/1402.5816

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