On the uniqueness of even $L^p$ Minkowski problem
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914112021200896 |
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| author | He, Weiyong Liu, Junbang |
| author_facet | He, Weiyong Liu, Junbang |
| contents | We prove that there is a unique $p_0\in [0,1)$, which can be characterized by the eigenvalue of Hilbert operator related to a convex body, that the even $L^p$ Minkowski problem has a unique solution for $p\geq p_0$, and the uniqueness fails for infinitely many convex bodies if $p<p_0$. The previous results by many experts in the field assert that the uniqueness holds for $p>p_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21530 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the uniqueness of even $L^p$ Minkowski problem He, Weiyong Liu, Junbang Metric Geometry Analysis of PDEs Differential Geometry We prove that there is a unique $p_0\in [0,1)$, which can be characterized by the eigenvalue of Hilbert operator related to a convex body, that the even $L^p$ Minkowski problem has a unique solution for $p\geq p_0$, and the uniqueness fails for infinitely many convex bodies if $p<p_0$. The previous results by many experts in the field assert that the uniqueness holds for $p>p_0$. |
| title | On the uniqueness of even $L^p$ Minkowski problem |
| topic | Metric Geometry Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2510.21530 |