Iterations of curvature images

Mohammad N. Ivaki

doi:10.1112/mtk.12037

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arXiv · 1911.04534

Iterations of curvature images

Mohammad N. Ivaki

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Abstract

We study the iterations of a class of curvature image operators $\Lambda_p^{\varphi}$ 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 $\varphi$. One of our results states that if $p\in (-n,1)$ and $\varphi$ 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.

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Mohammad N. Ivaki. 2019-11-11. Iterations of curvature images. https://doi.org/10.1112/mtk.12037

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