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| 27-01-2004 |
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Unit of Mathematics - Seminar: "On isoperimetric dimensions of product spaces"
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Speaker: Daniel Levin, Technion - Israel Institute of Technology, Haifa
Title: On isoperimetric dimensions of product spaces
Date & Time: Tuesday, January 27, at 14:15
Place: Seminar room, ORT Braude College, Karmiel
Refreshments: 14:00
Abstract: It is well-known that dimensions of Euclidean spaces add up,
if one considers their product, ${\Bbb{R}}^d={\Bbb{R}}^m
\times {\Bbb{R}}^n$, $d=m+n$. For Riemannian manifolds,
the notion of dimension is more delicate, e.g. the
topological dimension does not reflect their geometry at
infinity. However, one may introduce {\it an isoperimetric
dimension} through isoperimetric inequalities.
The dimension introduced in this way is not a number but a
family of functions indexed by a parameter $p$, $1 < p < \ infty$.
Our main result generalizes the addition of dimensions in the
euclidean case using the notion of the isoperimetric dimension.
(This is a joint work with T. Coulhon and A. Grigor'yan).
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