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Ends of metric measure spaces and Sobolev inequalities. (English) Zbl 1086.58021
Summary: Generalizing work of Li and Wang, we prove sharp volume growth/decay rates for ends of metric measure spaces supporting a $\left(p,p\right)$-Sobolev inequality. A sharp result for $\left(q,p\right)$-Sobolev inequalities is also proved.
##### MSC:
 58J99 Partial differential equations on manifolds; differential operators 58J50 Spectral problems; spectral geometry; scattering theory
##### References:
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