Transactions of the American Mathematical Society

Author(s): Panos Papasoglu
Journal: Trans. Amer. Math. Soc. 361 (2009), 5139-5162.
MSC (2000): Primary 53C20, 53C23, 20F65
Posted: May 19, 2009
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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

such that minimizers in dimension 3 have genus at most

, then the filling function in dimension 3 is `almost' linear.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 53C20, 53C23, 20F65

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

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

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