Ahlfors Bers Colloquium
May
19-22, 2005
University of
Michigan
Ann Arbor, Michigan
Registration
Organizers
Dick
Canary
Juha
Heinonen
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Workshop
Abstract Detail
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Raanan Schul Yale University
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A characterization of subsets of finite length curves in Hilbert space and the analyst's TSP
We characterize subsets of Hilbert space that are contained in a curve of finite length. We do so by extending and improving results of Peter Jones and Kate Okikiolu for sets in $\R^d$. Their results formed the basis of quantitative rectifiability in $\R^d$. In the talk we will explain the following statement which we obtain: given a set $K$ , $\diam(K) +\sum\beta^2(Q)diam(Q) \sim \ell(\Gamma_{MST})$. Here $\beta$ (the Jones $\beta$ number) is taken with respect to $K$, the sum is over a multiresolutional family of (overlapping) balls $Q$ centered on $K$, and $\Gamma_{MST}$ is the shortest connected set containing $K$. | ||
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