Geometric Analysis and Topology Seminar

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Lipschitz graphs in Carnot groups

Speaker: Davide Vittone, University of Padova

Location: Warren Weaver Hall 512

Date: Friday, October 27, 2023, 11 a.m.

Synopsis:

Submanifolds with intrinsic Lipschitz regularity in Carnot groups (i.e., stratified groups endowed with a sub-Riemannian structure) can be introduced using the theory of intrinsic Lipschitz graphs started years ago by B. Franchi, R. Serapioni and F. Serra Cassano. One of the main questions concerns a Rademacher-type theorem about the almost everywhere existence of a tangent plane to intrinsic Lipschitz graphs: after a gentle introduction to the topic, I will discuss a positive solution to the problem in Heisenberg groups. The proof uses the language of currents in Heisenberg groups (in particular, a version of the Constancy Theorem) and a number of complementary results such as extension and smooth approximation theorems for intrinsic Lipschitz graphs. I will also show a recent example, joint with A. Julia and S. Nicolussi Golo, of an intrinsic Lipschitz graph in a Carnot group that is nowhere intrinsically differentiable. The talk will be kept at an introductory level.