
TL;DR
This paper investigates the iterative behavior of a class of curvature image operators related to the $L_p$ Minkowski problem, establishing convergence results under specific conditions on parameters and data symmetry.
Contribution
It extends understanding of curvature image operators by proving convergence of their iterations to fixed points for certain parameter ranges and symmetry conditions.
Findings
Iterative sequences converge in Hausdorff distance to fixed points.
Convergence occurs for specific ranges of p and symmetric data.
Fixed points solve the $L_p$ Minkowski problem with prescribed data.
Abstract
We study the iterations of a class of curvature image operators introduced by the author in (J. Funct. Anal. 271 (2016) 2133--2165). The fixed points of these operators are the solutions of the Minkowski problems with the positive continuous prescribed data . One of our results states that if and is even, or if , then the iterations of these operators applied to suitable convex bodies sequentially converge in the Hausdorff distance to fixed points.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
