Rank-one theorem and subgraphs of BV functions in Carnot groups
2019
Abstract We prove a rank-one theorem a 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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