Analysis Seminar: Mauricio Godoy Molina
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Speaker: Mauricio Godoy Molina, Postdoc, Mathematical Department, UiB.
Title: Capacity and energy
Abstract: The aim of this week's seminar is to introduce the Riesz $s$-capacity of a subset of Euclidean space and use it to deduce some good behavior of "small" sets, i.e., geometrically speaking, Radon measures shouldn't be too concentrated on small regions. As a consequence of this capacitarian approach (plus some technical details left behind in prior seminars), we will obtain formulas for the Hausdorff dimension of products of sets, and we will show that for any set $A$ of Radon measure $t>0$ and any $0<s<t$, there exists a subset of $A$ with Radon measure $s$.
Title: Capacity and energy
Abstract: The aim of this week's seminar is to introduce the Riesz $s$-capacity of a subset of Euclidean space and use it to deduce some good behavior of "small" sets, i.e., geometrically speaking, Radon measures shouldn't be too concentrated on small regions. As a consequence of this capacitarian approach (plus some technical details left behind in prior seminars), we will obtain formulas for the Hausdorff dimension of products of sets, and we will show that for any set $A$ of Radon measure $t>0$ and any $0<s<t$, there exists a subset of $A$ with Radon measure $s$.
20.01.2015