Analysis and Geometric Analysis Seminar

Antoine JuliaUniversité Paris-Saclay
Surfaces and (intrinsic) graphs in Heisenberg and Carnot groups

Monday, February 14, 2022 - 2:40pm
Malott 406

Carnot groups, and in particular the Heisenberg groups, are metric spaces with a lot of additional structure, so that many notions of analysis and geometry have analogues in that setting. For instance, one can study sets of finite perimeter in these groups. Doing just this, Franchi, Serapioni and Serra Cassano proved in the early 2000' that their boundary could be covered by 'intrinsic Lipschitz graphs'. These are a non-abelian version of euclidean Lipschitz graphs, which makes this result a counterpart of De Giorgi's Structure Theorem for euclidean sets of finite perimeter. Analysis of these objects turned out to be quite challenging and has found a surprising application in the recent works of Naor and Young. I will present some of the results and open questions about intrinsic Lipschitz graphs.