Displacement Lipschitz Spaces and Rectifiability

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2024_rm_tojo_displacement.pdf (579.22 KB)
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URI: https://hdl.handle.net/10347/46478
ISSN: 1422-6383
E-ISSN: 1420-9012
DOI: 10.1007/S00025-024-02315-Z

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2024-12-13

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Springer
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In 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.

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Arc length| Convexity| Curvature| Lipschitz space| Rectifiability

Bibliographic citation

Tojo, F. A. F. (2025). Displacement Lipschitz Spaces and Rectifiability. Results in Mathematics, 80(1). https://doi.org/10.1007/S00025-024-02315-Z

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The author was partially supported by Grant PID2020-113275GB-I00 funded by MCIN/AEI/10.13039/501100011033, Spain, and by “ERDF A way of making Europe” of the “European Union”; and by Xunta de Galicia, Spain, project (ED431C 2023/12).

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Copyright: 2024 The Author(s)
Attribution-NonCommercial-NoDerivatives 4.0 International

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Estatística, Análise Matemática e Optimización
Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)