Calculus of Variations and Geometric Measure Theory

A. Julia - S. Nicolussi Golo - D. Vittone

Lipschitz functions on submanifolds in Heisenberg groups

created by vittone on 14 Jul 2021
modified on 24 Mar 2022


Accepted Paper

Inserted: 14 jul 2021
Last Updated: 24 mar 2022

Journal: Int. Math. Res. Not. IMRN
Year: 2022

ArXiv: 2107.00515 PDF


We study the behavior of Lipschitz functions on intrinsic $C^1$ submanifolds of Heisenberg groups: our main result is their almost everywhere tangential Pansu differentiability. We also provide two applications: a Lusin-type approximation of Lipschitz functions on $\mathbb H$-rectifiable sets, and a coarea formula on $\mathbb H$-rectifiable sets that completes the program started in $[16]$.