The Dual Minkowski Problem under Group Actions
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914614045835264 |
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| author | Shan, Junjie |
| author_facet | Shan, Junjie |
| contents | In this paper, we study the dual Minkowski problem under group symmetry. For $0<q\le n$, we give a complete existence characterization in the framework of $G$-invariant convex bodies when the group $G\subset O(n)$ has no nonzero fixed points, recovering the origin-symmetric setting when $G=\{\pm I\}$. The necessary and sufficient conditions concern the concentration of the measure on $G$-invariant subspaces, both in the range $0<q<n$ and at the critical endpoint $q=n$, where the problem becomes the logarithmic Minkowski problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15891 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Dual Minkowski Problem under Group Actions Shan, Junjie Metric Geometry In this paper, we study the dual Minkowski problem under group symmetry. For $0<q\le n$, we give a complete existence characterization in the framework of $G$-invariant convex bodies when the group $G\subset O(n)$ has no nonzero fixed points, recovering the origin-symmetric setting when $G=\{\pm I\}$. The necessary and sufficient conditions concern the concentration of the measure on $G$-invariant subspaces, both in the range $0<q<n$ and at the critical endpoint $q=n$, where the problem becomes the logarithmic Minkowski problem. |
| title | The Dual Minkowski Problem under Group Actions |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2605.15891 |