Limiting shape of the $L_p$-Minkowski problem
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929685475098624 |
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| author | Du, Shi-Zhong Wang, Xu-Jia Zhu, Baocheng |
| author_facet | Du, Shi-Zhong Wang, Xu-Jia Zhu, Baocheng |
| contents | Ben Andrews classified the limiting shape for isotropic curvature flow corresponding to the solutions of the $L_p$-Minkowski problem as $p\to-\infty$ in the planar case. In this paper, we use the group-invariant method to study the asymptotic shape of solutions to the $L_p$-Minkowski problem as $p\to-\infty$ in high dimensions. For any regular polytope $T$, we establish the existence of a solution ${Ω^{(p)}}$ to the $L_p$-Minkowski problem that converges to $T$ as $p\to-\infty$, thereby revealing the intricate geometric structure underlying this limiting behavior. We also extend the result to the dual Minkowski problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14226 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limiting shape of the $L_p$-Minkowski problem Du, Shi-Zhong Wang, Xu-Jia Zhu, Baocheng Analysis of PDEs Differential Geometry Ben Andrews classified the limiting shape for isotropic curvature flow corresponding to the solutions of the $L_p$-Minkowski problem as $p\to-\infty$ in the planar case. In this paper, we use the group-invariant method to study the asymptotic shape of solutions to the $L_p$-Minkowski problem as $p\to-\infty$ in high dimensions. For any regular polytope $T$, we establish the existence of a solution ${Ω^{(p)}}$ to the $L_p$-Minkowski problem that converges to $T$ as $p\to-\infty$, thereby revealing the intricate geometric structure underlying this limiting behavior. We also extend the result to the dual Minkowski problem. |
| title | Limiting shape of the $L_p$-Minkowski problem |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2501.14226 |