Cheeger constants of surfaces and isoperimetric inequalities
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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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 5139-5162
- MSC (2000): Primary 53C20, 53C23, 20F65
- DOI: https://doi.org/10.1090/S0002-9947-09-04815-6
- MathSciNet review: 2515806