An expanding curvature flow and the (p,q)-Christoffel-Minkowski problems
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916299386388480 |
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| author | Chen, Bin Cui, Jingshi Zhao, Peibiao |
| author_facet | Chen, Bin Cui, Jingshi Zhao, Peibiao |
| contents | The present paper introduces a new class of geometric measures, the k-th (p,q)-mixed curvature measures, and a natural correspondence-(p,q)-Christoffel-Minkowski problem is proposed. The (p,q)-Christoffel-Minkowski problem posed here can be regarded as a natural generalization of the L_p Christoffel-Minkowski problem and Lp dual Minkowski problem.
We investigate and arrive at the existence of smooth solution to the (p,q)-Christoffel-Minkowski problem by a type of expanding curvature flow. Furthermore, the uniqueness result of solutions to the (p,q)-Christoffel-Minkowski problem shall be discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_05105 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An expanding curvature flow and the (p,q)-Christoffel-Minkowski problems Chen, Bin Cui, Jingshi Zhao, Peibiao Differential Geometry Analysis of PDEs The present paper introduces a new class of geometric measures, the k-th (p,q)-mixed curvature measures, and a natural correspondence-(p,q)-Christoffel-Minkowski problem is proposed. The (p,q)-Christoffel-Minkowski problem posed here can be regarded as a natural generalization of the L_p Christoffel-Minkowski problem and Lp dual Minkowski problem. We investigate and arrive at the existence of smooth solution to the (p,q)-Christoffel-Minkowski problem by a type of expanding curvature flow. Furthermore, the uniqueness result of solutions to the (p,q)-Christoffel-Minkowski problem shall be discussed. |
| title | An expanding curvature flow and the (p,q)-Christoffel-Minkowski problems |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2203.05105 |