Calculus of Variations and Geometric Measure Theory
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Workshop MAR: Metric Analysis and Regularity

Rectifiability issues in sub-Riemannian geometry

Davide Vittone (Dip. Matematica, Univ. di Padova)

created by dimarino on 18 Sep 2018

Abstract.

In this talk we discuss two problems concerning "rectifiability" in sub-Riemannian geometry and particularly in the model setting of Carnot groups. The first problem regards the rectifiability of boundaries of sets with finite perimeter in Carnot groups, while the second one concerns Rademacher-type results (existence of a tangent plane out of a negligible set) for (intrinsic) graphs with (intrinsic) Lipschitz regularity. We will introduce both problems and discuss the state-of-the-art. Eventually, we will present some recent results about the rectifiability of sets with finite perimeter in a certain class of Carnot groups (including the simplest open case, i.e., the Engel group) and about a Rademacher theorem for intrinsic Lipschitz graphs in Heisenberg groups.

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