Fernández Tojo, Fernando Adrián2026-03-242026-03-242024-12-13Tojo, F. A. F. (2025). Displacement Lipschitz Spaces and Rectifiability. Results in Mathematics, 80(1). https://doi.org/10.1007/S00025-024-02315-Z1422-6383https://hdl.handle.net/10347/46478In this article, we introduce the notion of displacement Lipschitz spaces based on a divided difference approach. After studying rectifiability and arc length in displacement spaces, we apply Lipschitz functions to the study of convexity by measuring the allowed curvature of paths.engCopyright: 2024 The Author(s)Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Arc lengthConvexityCurvatureLipschitz spaceRectifiabilityjournal article2025-12-0410.1007/S00025-024-02315-Z1420-9012open access1420-9012