# Rank-one theorem and subgraphs of BV functions in Carnot groups

created by vittone on 06 Dec 2017
modified on 17 Nov 2020

[BibTeX]

Published Paper

Inserted: 6 dec 2017
Last Updated: 17 nov 2020

Journal: J. Funct. Anal.
Volume: 276
Pages: 687–715
Year: 2019
Doi: http://dx.doi.org/10.1016/j.jfa.2018.09.016

Abstract:

We prove a rank-one theorem à la G. Alberti for the derivatives of vector-valued maps with bounded variation in a class of Carnot groups that includes Heisenberg groups $\mathbb H^n$ for $n\geq 2$. The main tools are properties relating the horizontal derivatives of a real-valued function with bounded variation and its subgraph.