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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on some classical results of Gromov-Lawson


Author: Mostafa Esfahani Zadeh
Journal: Proc. Amer. Math. Soc. 140 (2012), 3663-3672
MSC (2000): Primary 58J22; Secondary 19K56, 46L80, 53C21, 53C27
Published electronically: March 5, 2012
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Abstract: In this paper we show how the higher index theory can be used to prove results concerning the non-existence of a complete Riemannian metric with uniformly positive scalar curvature at infinity. By improving some classical results due to M. Gromov and B. Lawson we show the efficiency of these methods to prove such non-existence theorems.


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Additional Information

Mostafa Esfahani Zadeh
Affiliation: Department of Mathematical Science, Sharif University of Technology, Tehran, Iran – and – School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran
Email: esfahani@sharif.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11544-8
PII: S 0002-9939(2012)11544-8
Keywords: Higher index theory, enlargeability, Dirac operators.
Received by editor(s): December 23, 2009
Received by editor(s) in revised form: April 4, 2011
Published electronically: March 5, 2012
Additional Notes: This research was in part supported by a grant from IPM (No. 89510130).
Communicated by: Varghese Mathai
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.