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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 short proof of Gromov's filling inequality


Author: Stefan Wenger
Journal: Proc. Amer. Math. Soc. 136 (2008), 2937-2941
MSC (2000): Primary 53C23
Published electronically: April 7, 2008
MathSciNet review: 2399061
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Abstract: We give a very short and rather elementary proof of Gromov's filling volume inequality for $ n$-dimensional Lipschitz cycles (with integer and $ \mathbb{Z}_2$-coefficients) in $ L^\infty$-spaces. This inequality is used in the proof of Gromov's systolic inequality for closed aspherical Riemannian manifolds and is often regarded as the difficult step therein.


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Additional Information

Stefan Wenger
Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
Email: wenger@cims.nyu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09203-4
PII: S 0002-9939(08)09203-4
Keywords: Systolic inequality, isoperimetric inequality, Lipschitz chains
Received by editor(s): March 29, 2007
Published electronically: April 7, 2008
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.