Quantitative decompositions of Lipschitz mappings into metric spaces

• DOI: 10.1090/tran/8930
• Publication Date: 2023-03-15T14:27:14Z
• Authors: Guy David; Raanan Schul
• Keywords: Lipschitz domain; Metric differential

We study the quantitative properties of Lipschitz mappings from Euclidean spaces into metric spaces. prove that it is always possible to decompose domain such a mapping pieces on which “behaves like projection mapping” along with “garbage set” <bold>arbitrarily small</bold> in an appropriate sense. Moreover, our control quantitative, i.e., independent both particular and space maps into. This improves theorem Azzam-Schul paper “Hard Sard”, answers question left open paper. The proof uses ideas differentiation, as well detailed how supplement by additional coordinates form bi-Lipschitz mappings.