A short proof of Gromov’s filling inequality
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- by Stefan Wenger PDF
- Proc. Amer. Math. Soc. 136 (2008), 2937-2941 Request permission
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.References
- Luigi Ambrosio and Bernd Kirchheim, Currents in metric spaces, Acta Math. 185 (2000), no. 1, 1–80. MR 1794185, DOI 10.1007/BF02392711
- Mikhael Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983), no. 1, 1–147. MR 697984
- Bernd Kirchheim, Rectifiable metric spaces: local structure and regularity of the Hausdorff measure, Proc. Amer. Math. Soc. 121 (1994), no. 1, 113–123. MR 1189747, DOI 10.1090/S0002-9939-1994-1189747-7
- S. Wenger, Isoperimetric inequalities of Euclidean type in metric spaces, Geom. Funct. Anal. 15 (2005), no. 2, 534–554. MR 2153909, DOI 10.1007/s00039-005-0515-x
Additional Information
- Stefan Wenger
- Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
- MR Author ID: 764752
- ORCID: 0000-0003-3645-105X
- Email: wenger@cims.nyu.edu
- Received by editor(s): March 29, 2007
- Published electronically: April 7, 2008
- Communicated by: Jon G. Wolfson
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2937-2941
- MSC (2000): Primary 53C23
- DOI: https://doi.org/10.1090/S0002-9939-08-09203-4
- MathSciNet review: 2399061