Calculus of Variations and Geometric Measure Theory
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Rectifiable measures: a local-to-global adventure tailored for Carnot groups

Gioacchino Antonelli

created by pinamonti on 27 Jan 2021
modified on 09 Feb 2021

11 feb 2021 -- 15:00   [open in google calendar]

Zoom Seminar

Anyone interested to attend the seminar has to send an email to Andrea.pinamonti@unitn.it

Abstract.

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.

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