The $L_{p}$ Dual Minkowski Problem for Group-Invariant Convex Bodies
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866918202761543680 |
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| author | Shan, Junjie |
| author_facet | Shan, Junjie |
| contents | In this paper, we study the $L_p$ dual Minkowski problem for all $q, p \in \mathbb{R}$ from an algebraic perspective. We establish the existence of solutions for group-invariant convex bodies (not necessarily origin-symmetric), thereby covering three fundamental problems as special cases: the $L_p$ Minkowski problem ($q = n$), the $L_p$ Aleksandrov problem ($q = 0$), and the dual Minkowski problem ($p = 0$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13233 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $L_{p}$ Dual Minkowski Problem for Group-Invariant Convex Bodies Shan, Junjie Metric Geometry In this paper, we study the $L_p$ dual Minkowski problem for all $q, p \in \mathbb{R}$ from an algebraic perspective. We establish the existence of solutions for group-invariant convex bodies (not necessarily origin-symmetric), thereby covering three fundamental problems as special cases: the $L_p$ Minkowski problem ($q = n$), the $L_p$ Aleksandrov problem ($q = 0$), and the dual Minkowski problem ($p = 0$). |
| title | The $L_{p}$ Dual Minkowski Problem for Group-Invariant Convex Bodies |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2507.13233 |