Title: Invertible Homogeneous Metric Spaces
Speaker: David Freeman (University of Cincinnati Blue Ash College)
Time: Friday, October 10, 2014 at 3:00 pm
Place: MSB 109A
Abstract: What geometric and/or analytic properties characterize Euclidean space?
More precisely, what conditions are necessary and sufficient to imply that a given
metric space can be mapped onto a Euclidean space with bi-Lipschitz distortion? In
light of this question we consider the fact that Euclidean space is isometrically
homogeneous and can be “inverted” by way of Moebius transformations. It turns out
that metric generalizations of such homogeneity and invertibility can be used to
characterize Euclidean space within certain classes of metric spaces. We will frame
such characterizations of Euclidean space within the broader context of recent
efforts to obtain geometric/analytic characterizations of the boundaries of
canonical hyperbolic spaces.
Hoping to see you,
Iddo
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