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

created by vittone on 06 Dec 2017
modified on 22 Oct 2018

[BibTeX]

Accepted Paper

Inserted: 6 dec 2017
Last Updated: 22 oct 2018

Journal: Journal of Functional Analysis
Year: 2018

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.