Iterations of curvature images
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866908425549512704 |
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| author | Ivaki, Mohammad N. |
| author_facet | Ivaki, Mohammad N. |
| contents | We study the iterations of a class of curvature image operators $Λ_p^φ$ introduced by the author in (J. Funct. Anal. 271 (2016) 2133--2165). The fixed points of these operators are the solutions of the $L_p$ Minkowski problems with the positive continuous prescribed data $φ$. One of our results states that if $p\in (-n,1)$ and $φ$ is even, or if $p\in (-n,-n+1]$, then the iterations of these operators applied to suitable convex bodies sequentially converge in the Hausdorff distance to fixed points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_04534 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Iterations of curvature images Ivaki, Mohammad N. Metric Geometry Analysis of PDEs Differential Geometry We study the iterations of a class of curvature image operators $Λ_p^φ$ introduced by the author in (J. Funct. Anal. 271 (2016) 2133--2165). The fixed points of these operators are the solutions of the $L_p$ Minkowski problems with the positive continuous prescribed data $φ$. One of our results states that if $p\in (-n,1)$ and $φ$ is even, or if $p\in (-n,-n+1]$, then the iterations of these operators applied to suitable convex bodies sequentially converge in the Hausdorff distance to fixed points. |
| title | Iterations of curvature images |
| topic | Metric Geometry Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/1911.04534 |