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 H^n for n ≥ 2. The main tools are properties relating the horizontal derivatives of a real-valued function with bounded variation and its subgraph.
Rank-one theorem and subgraphs of BV functions in Carnot groups
DON, SEBASTIANO;MASSACCESI, ANNALISA;Davide Vittone
2019
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 H^n for n ≥ 2. The main tools are properties relating the horizontal derivatives of a real-valued function with bounded variation and its subgraph.
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