Global Lipschitz extension preserving the slope
Metric Geometry
2025-07-29 v1 Functional Analysis
Abstract
We show that every real-valued Lipschitz function on a subset of a metric space can be extended to the whole space while preserving the slope and, up to a small error, the global Lipschitz constant. This answers a question posed by Di Marino, Gigli, and Pratelli, who established the analogous property for the asymptotic Lipschitz constant. We also prove the same result for the ascending slope and for the descending slope.
Keywords
Cite
@article{arxiv.2507.20642,
title = {Global Lipschitz extension preserving the slope},
author = {Nicolò De Ponti and Jacopo Somaglia},
journal= {arXiv preprint arXiv:2507.20642},
year = {2025}
}