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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Cheeger constants of surfaces and isoperimetric inequalities


Author: Panos Papasoglu
Journal: Trans. Amer. Math. Soc. 361 (2009), 5139-5162
MSC (2000): Primary 53C20, 53C23, 20F65
Published electronically: May 19, 2009
MathSciNet review: 2515806
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Abstract: We show that if the isoperimetric profile of a bounded genus non-compact surface grows faster than $ \sqrt t$, then it grows at least as fast as a linear function. This generalizes a result of Gromov for simply connected surfaces.

We study the isoperimetric problem in dimension 3. We show that if the filling volume function in dimension 2 is Euclidean, while in dimension 3 it is sub-Euclidean and there is a $ g$ such that minimizers in dimension 3 have genus at most $ g$, then the filling function in dimension 3 is `almost' linear.


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Additional Information

Panos Papasoglu
Affiliation: Department of Mathematics, University of Athens, Athens 157 84, Greece
Email: panos@math.uoa.gr

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04815-6
PII: S 0002-9947(09)04815-6
Received by editor(s): August 3, 2007
Published electronically: May 19, 2009
Additional Notes: This work was co-funded by the European Social Fund (75%) and the National Resources (25%) (Epeaek II) Pythagoras
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.