Séminaire Analyse Harmonique
Square packings and rectifiable doubling measures
Dec. 2023
Intervenant : Matthew Badger
Institution : University of Connecticut
Heure : 14h00 - 15h00
Lieu : salle 2L8

I will report on some recent progress on the problem of characterizing sets which lie in the image of a Lipschitz map from the plane into $3$-dimensional Euclidean space. The new construction of Lipschitz maps is based on a simple observation about square packings. As an application, in any complete Ahlfors $q$-regular metric space with $q>m-1$, we construct an abundance of $m$-rectifiable doubling measures that are purely $(m-1)$-unrectifiable. Moreover, it is possible to prescribe the lower and upper Hausdorff and packing dimensions of the measures. This is joint work with Raanan Schul.

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