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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 $(p,p)$-Sobolev inequality. A sharp result for $(q,p)$-Sobolev inequalities is also proved.

58J99Partial differential equations on manifolds; differential operators
58J50Spectral problems; spectral geometry; scattering theory
Full Text: DOI
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