Ressource pédagogique : Robert Young - Quantitative rectifiability and differentiation in the Heisenberg group

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(joint work with Assaf Naor) The Heisenberg group $mathbb{H}$ is a sub-Riemannian manifold that is unusually difficult to embed in $mathbb{R}^n$. Cheeger and Kleiner introduced a new notion of differentiation that they used to show that it does not embed nicely into $L_1$. This notion is based on surfaces in $mathbb{H}$, and in this talk, we will describe new techniques that let us quantify the "roughness" of such surfaces, find sharp bounds on the distortion of embeddings of $mathbb{H}$, and estimate the accuracy of an approximate algorithm for the Sparsest Cut Problem.

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