On the number of solutions to the planar dual Minkowski problem
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913447625621504 |
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| author | Liu, YanNan Lu, Jian |
| author_facet | Liu, YanNan Lu, Jian |
| contents | The dual Minkowski problem in the two-dimensional plane is studied in this paper. By combining the theoretical analysis and numerical estimation of an integral with parameters, we find the number of solutions to this problem for the constant dual curvature case when $0<q\leq4$. An improved nonuniqueness result when $q>4$ is also obtained. As an application, a result on the uniqueness and nonuniqueness of solutions to the $L_p$-Alexandrov problem is obtained for $p<0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_15385 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the number of solutions to the planar dual Minkowski problem Liu, YanNan Lu, Jian Analysis of PDEs Differential Geometry The dual Minkowski problem in the two-dimensional plane is studied in this paper. By combining the theoretical analysis and numerical estimation of an integral with parameters, we find the number of solutions to this problem for the constant dual curvature case when $0<q\leq4$. An improved nonuniqueness result when $q>4$ is also obtained. As an application, a result on the uniqueness and nonuniqueness of solutions to the $L_p$-Alexandrov problem is obtained for $p<0$. |
| title | On the number of solutions to the planar dual Minkowski problem |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2209.15385 |