Iterations of curvature images

Abstract

We study the iterations of a class of curvature image operators ${\Lambda }_p^{\phi }$ 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 $\phi$. One of our results states that if $p\in (-n,1)$ and $\phi$ 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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References in corpus (6)

• The Logarithmic Minkowski Problem
• The $L_p$-Minkowski problem for $-n<p<1$
• A unified flow approach to smooth, even $L_p$-Minkowski problems
• Smoothness in the $l_p$ Minkowski problem for $p<1$
• The second mixed projection problem and the projection centroid conjectures
• A local uniqueness theorem for minimizers of Petty's conjectured projection inequality

Cited by in corpus (2)

• Orlicz-Minkowski flows
• Parabolic approaches to curvature equations