Global Lipschitz extension preserving the slope
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911079665238016 |
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| author | De Ponti, Nicolò Somaglia, Jacopo |
| author_facet | De Ponti, Nicolò Somaglia, Jacopo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Lipschitz extension preserving the slope De Ponti, Nicolò Somaglia, Jacopo Metric Geometry Functional Analysis 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. |
| title | Global Lipschitz extension preserving the slope |
| topic | Metric Geometry Functional Analysis |
| url | https://arxiv.org/abs/2507.20642 |