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Antonelli: Rectifiable measures: a local-to-global adventure tailored for Carnot groups

Antonelli: Anyone interested to attend the seminar has to send an email to Andrea.pinamonti@unitn.it
I will discuss the rectifiability of measures in Carnot groups. First, I will recall basic notions about rectifiability, and Carnot groups. Hence, I will introduce the new notion of P-rectifiable measure in Carnot groups: a P-rectifiable measure is a measure with good density properties for which the tangent measures are "flat" almost everywhere. I will discuss some of the main structure results within this class of measures, and at the end I will state a MarstrandMattila rectifiability criterion for P-rectifiable measures with tangents that are complemented by a normal subgroup. I will finally show how the latter rectifiability criterion allows to give a proof of the celebrated Preiss' theorem for one-dimensional measures in the first Heisenberg group H1 . This is a joint work with Andrea Merlo.
http://cvgmt.sns.it/seminar/772/
When
Thu Feb 11, 2021 2pm – 3pm Coordinated Universal Time
Where
Zoom Seminar (map)