The $L_p$ chord Minkowski problem for super-critical exponent
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916983192158208 |
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| author | Chen, Shibing Li, Qi-Rui Li, Yuanyuan |
| author_facet | Chen, Shibing Li, Qi-Rui Li, Yuanyuan |
| contents | The $L_p$ chord Minkowski problem was recently introduced by Lutwak, Xi, Yang and Zhang, which seeks to determine the necessary and sufficient conditions for a given finite Borel measure such that it is the $L_p$ chord measure of a convex body. In this paper, we solve the $L_p$ chord Minkowski problem for the super-critical exponents by combining a nonlocal Gauss curvature flow introduced in \cite{HHLW exi} and a topological argument developed in \cite{GLW2022}. Notably, we provide a simplified argument for the topological part. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01084 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $L_p$ chord Minkowski problem for super-critical exponent Chen, Shibing Li, Qi-Rui Li, Yuanyuan Analysis of PDEs 35A15 F.2.2; G.1.8 The $L_p$ chord Minkowski problem was recently introduced by Lutwak, Xi, Yang and Zhang, which seeks to determine the necessary and sufficient conditions for a given finite Borel measure such that it is the $L_p$ chord measure of a convex body. In this paper, we solve the $L_p$ chord Minkowski problem for the super-critical exponents by combining a nonlocal Gauss curvature flow introduced in \cite{HHLW exi} and a topological argument developed in \cite{GLW2022}. Notably, we provide a simplified argument for the topological part. |
| title | The $L_p$ chord Minkowski problem for super-critical exponent |
| topic | Analysis of PDEs 35A15 F.2.2; G.1.8 |
| url | https://arxiv.org/abs/2510.01084 |