|
A short proof of Gromov's filling inequality
Author(s):
Stefan
Wenger
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2937-2941.
MSC (2000):
Primary 53C23
Posted:
April 7, 2008
MathSciNet review:
2399061
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We give a very short and rather elementary proof of Gromov's filling volume inequality for  -dimensional Lipschitz cycles (with integer and  -coefficients) in  -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:
-
- 1.
- L. Ambrosio, B. Kirchheim: Currents in metric spaces, Acta Math. 185 (2000), no. 1, 1-80. MR 1794185 (2001k:49095)
- 2.
- M. Gromov: Filling Riemannian manifolds, J. Differential Geom. 18 (1983), no. 1, 1-147. MR 697984 (85h:53029)
- 3.
- B. Kirchheim: Rectifiable metric spaces: local structure and regularity of the Hausdorff measure, Proc. Amer. Math. Soc. 121 (1994), no. 1, 113-123. MR 1189747 (94g:28013)
- 4.
- S. Wenger: Isoperimetric inequalities of Euclidean type in metric spaces, Geom. Funct. Anal. 15 (2005), no. 2, 534-554. MR 2153909 (2006d:53039)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
53C23
Retrieve articles in all Journals with
MSC (2000):
53C23
Additional Information:
Stefan
Wenger
Affiliation:
Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
Email:
wenger@cims.nyu.edu
DOI:
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
Posted:
April 7, 2008
Communicated by:
Jon G. Wolfson
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
