The connectivity at infinity of a manifold and Sobolev inequalities

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,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.


Published in:
Expositiones Mathematicae, 32, 4, 365-383
Year:
2014
Publisher:
Jena, Elsevier
ISSN:
0723-0869
Keywords:
Laboratories:




 Record created 2015-04-13, last modified 2018-03-17

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