The connectivity at infinity of a manifold and Sobolev inequalities

Pigola, StefanoSetti, Alberto G.Troyanov, Marc2015-04-132015-04-132015-04-13201410.1016/j.exmath.2013.12.006https://infoscience.epfl.ch/handle/20.500.14299/113042WOS:000349739100002The 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,L-p-Sobolev inequality (2 <= p, q <= p*), provided the negative part of its Ricci tensor is small (in a suitable spectral sense). In the route, we discuss potential theoretic properties of the ends of a manifold enjoying an L-q,L-p-Sobolev inequality. (C) 2013 Elsevier GmbH. All rights reserved.Ends of manifoldsSobolev inequalitiesRicci curvatureL-qL-p-cohomologyThe connectivity at infinity of a manifold and Sobolev inequalitiestext::journal::journal article::research article