Gauss curvature flow to the $L_p$-Gaussian chord Minkowski problem
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914864111288320 |
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| author | Zhao, Xia Zhao, Peibiao |
| author_facet | Zhao, Xia Zhao, Peibiao |
| contents | Recently, Huang and Qin \cite{HY01} introduced the Gaussian chord measure and $L_p$-Gaussian chord measure by variational methods. Meanwhile, they posed Gaussian chord Minkowski problem for $p=1$ and used variational methods to obtain an origin-symmetric normalized measure solution for the Gaussian chord Minkowski problem. The smooth solution, up to now, to the $L_p$-Gaussian chord Minkowski problem is still open.
Motivated by the forgoing works by Huang and Qin in \cite{HY01}, we propose in the present paper the $L_p(p>0)$-Gaussian chord Minkowski problem and log-Gaussian chord Minkowski problem, and obtain the smooth even solutions to these two types of problems by the method of a Gauss curvature flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05635 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gauss curvature flow to the $L_p$-Gaussian chord Minkowski problem Zhao, Xia Zhao, Peibiao Differential Geometry 52A20 \ \ 35K96\ \ 58J35 Recently, Huang and Qin \cite{HY01} introduced the Gaussian chord measure and $L_p$-Gaussian chord measure by variational methods. Meanwhile, they posed Gaussian chord Minkowski problem for $p=1$ and used variational methods to obtain an origin-symmetric normalized measure solution for the Gaussian chord Minkowski problem. The smooth solution, up to now, to the $L_p$-Gaussian chord Minkowski problem is still open. Motivated by the forgoing works by Huang and Qin in \cite{HY01}, we propose in the present paper the $L_p(p>0)$-Gaussian chord Minkowski problem and log-Gaussian chord Minkowski problem, and obtain the smooth even solutions to these two types of problems by the method of a Gauss curvature flow. |
| title | Gauss curvature flow to the $L_p$-Gaussian chord Minkowski problem |
| topic | Differential Geometry 52A20 \ \ 35K96\ \ 58J35 |
| url | https://arxiv.org/abs/2406.05635 |