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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.05206 |
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| _version_ | 1866910042446364672 |
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| author | De Bernardi, Carlo Alberto Veselý, Libor |
| author_facet | De Bernardi, Carlo Alberto Veselý, Libor |
| contents | Let $X$ be a normed space of a finite dimension at least two, and $C\subsetneq X$ a closed convex set with nonempty interior. We are interested in extending Lipschitz quasiconvex functions on $C$ to quasiconvex functions on $X$. We show that, unlike what holds for convex functions, in general one cannot obtain Lipschitz extensions (except for trivial cases). If we require just uniformly continuous or continuous extensions, such extendability properties for $C$ are shown to be characterized by some geometric properties of $C$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05206 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Extending quasiconvex functions from uniformly convex sets De Bernardi, Carlo Alberto Veselý, Libor Functional Analysis Let $X$ be a normed space of a finite dimension at least two, and $C\subsetneq X$ a closed convex set with nonempty interior. We are interested in extending Lipschitz quasiconvex functions on $C$ to quasiconvex functions on $X$. We show that, unlike what holds for convex functions, in general one cannot obtain Lipschitz extensions (except for trivial cases). If we require just uniformly continuous or continuous extensions, such extendability properties for $C$ are shown to be characterized by some geometric properties of $C$. |
| title | Extending quasiconvex functions from uniformly convex sets |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2603.05206 |