The Generalized Gaussian Minkowski Problem
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911962904920064 |
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| author | Liu, Jiaqian Tang, Shengyu |
| author_facet | Liu, Jiaqian Tang, Shengyu |
| contents | This article delves into the $L_p$ Minkowski problem within the framework of generalized Gaussian probability space. This type of probability space was initially introduced in information theory through the seminal works of Lutwak, Yang, and Zhang [49,50], as well as by Lutwak, Lv, Yang, and Zhang [45]. The primary focus of this article lies in examining the existence of this problem. While the variational method is employed to explore the necessary and sufficient conditions for the existence of the normalized Minkowski problem when $p \in \mathbb{R} \setminus \{0\}$, our main emphasis is on the existence of the generalized Gaussian Minkowski problem without the normalization requirement, particularly in the smooth category for $p \geq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14237 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Generalized Gaussian Minkowski Problem Liu, Jiaqian Tang, Shengyu Analysis of PDEs Probability 52A40, 52A38, 35J96 This article delves into the $L_p$ Minkowski problem within the framework of generalized Gaussian probability space. This type of probability space was initially introduced in information theory through the seminal works of Lutwak, Yang, and Zhang [49,50], as well as by Lutwak, Lv, Yang, and Zhang [45]. The primary focus of this article lies in examining the existence of this problem. While the variational method is employed to explore the necessary and sufficient conditions for the existence of the normalized Minkowski problem when $p \in \mathbb{R} \setminus \{0\}$, our main emphasis is on the existence of the generalized Gaussian Minkowski problem without the normalization requirement, particularly in the smooth category for $p \geq 1$. |
| title | The Generalized Gaussian Minkowski Problem |
| topic | Analysis of PDEs Probability 52A40, 52A38, 35J96 |
| url | https://arxiv.org/abs/2402.14237 |