Prescribed $L_p$ quotient curvature problem and related eigenvalue problem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910583341711360 |
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| author | Mei, Xinqun Wang, Guofang Weng, Liangjun |
| author_facet | Mei, Xinqun Wang, Guofang Weng, Liangjun |
| contents | In this paper, we investigate the existence of admissible (and strictly convex) smooth solutions to the prescribed $L_p$ quotient type curvature problem with $p>1$. For cases where $p=k-l+1$ and $p> k-l+1$, we obtain an admissible solution without any additional conditions, which is strictly spherically convex under a convexity condition. Under the same convexity condition, we establish the existence of a strictly spherically convex solution for the case $p<k-l+1$, provided that the prescribed function is even, a condition known to be necessary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12314 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Prescribed $L_p$ quotient curvature problem and related eigenvalue problem Mei, Xinqun Wang, Guofang Weng, Liangjun Analysis of PDEs Differential Geometry Primary: 35J96 Secondary: 35J60, 53C42, 58J05 In this paper, we investigate the existence of admissible (and strictly convex) smooth solutions to the prescribed $L_p$ quotient type curvature problem with $p>1$. For cases where $p=k-l+1$ and $p> k-l+1$, we obtain an admissible solution without any additional conditions, which is strictly spherically convex under a convexity condition. Under the same convexity condition, we establish the existence of a strictly spherically convex solution for the case $p<k-l+1$, provided that the prescribed function is even, a condition known to be necessary. |
| title | Prescribed $L_p$ quotient curvature problem and related eigenvalue problem |
| topic | Analysis of PDEs Differential Geometry Primary: 35J96 Secondary: 35J60, 53C42, 58J05 |
| url | https://arxiv.org/abs/2402.12314 |