By Guido De Philippis, SISSA, Trieste
I will show a general structure theorem for the singular part of A-free Radon measures, where A is a linear PDE operator. By applying the theorem to suitably chosen di erential operators A ,one can obtain a simple proof of Alberti's rank-one theorem and its extensions to functions of bounded defor-mation (BD). I will also show some consequences concerning the sharpness of Rademacher Theorem and the structure of Ambrosio{Kirchheim top-dimensional metric current in Rd.
