Differentiability of intrinsic Lipschitz graphs in Carnot groups

Abstract: Submanifolds with intrinsic Lipschitz regularity in sub-Riemannian Carnot groups can be introduced using the theory of intrinsic Lipschitz graphs started by B. Franchi, R. Serapioni and F. Serra Cassano almost 15 years ago. One of the main related questions concerns a Rademacher-type theorem (i.e., existence of a tangent plane) for such graphs: in this talk I will discuss a recent positive solution to the problem in Heisenberg groups. The proof uses currents in Heisenberg groups (in particular, a version of the celebrated 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.

differential geometrygeneral mathematicsgroup theorymetric geometryoptimization and controlsymplectic geometryspectral theory

Audience: researchers in the topic

( video )

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Sub-Riemannian Seminars

Series comments: The "Sub-Riemannian seminars" are the union of the "Séminaire de géométrie et analyse sous-riemannienne" (held in Paris since 2011) and the "International Sub-Riemannian Seminars", which were born in spring 2020 as a reaction to the COVID-19 pandemic.

The new format will gather every 3 weeks on average, alternating between these types of sessions:

- physical session in Paris (Laboratoire Jacques-Louis Lions), also transmitted online on Zoom.

- fully online session on Zoom.

- special session hosted physically somewhere else, and transmitted online.

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