Lipschitz parametrizations and Menger curvature in metric spaces

Pertti Mattila
University of Helsinki

I shall speak about the work of my student Immo Hahlomaa in Jyvaskyla. He has proved a version of one half of Peter Jones's travelling salesman theorem in metric spaces saying that the
finiteness of a Menger curvature sum, analogous to Jones's beta-sum, implies that the space is a Lipschitz image of a subset of the line. I
shall also discuss some related results.

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