Alberti's rank one theorem and quasiconformal mappings in metric measure spaces

We investigate a version of Alberti's rank one theorem in Ahlfors regular metric spaces, as well as a connection with quasiconformal mappings. More precisely, we give a proof of the rank one theorem that partially follows along the usual steps, but the most crucial step consists in showing for f E BV(X;Y) that at ||Df||s-a.e. x E X , the mapping f "behaves non-quasiconformally". (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.