The connectivity at infinity of a manifold and $L^{q,p}$-Sobolev inequalities

Stefano Pigola, Alberto G. Setti, Marc Troyanov

The purpose of this paper is to give a self-contained proof that a complete manifold with more than one end never supports an $L^{q,p}$-Sobolev inequality ($2\le p$, $q\leq p^{*}…