Stable solution of the log-Minkowski problem in the case of many hyperplane symmetries
Karoly J. Boroczky, Apratim De
TL;DR
This paper proves the stability of solutions to the Logarithmic Minkowski problem on the sphere when the problem exhibits symmetries with respect to multiple independent hyperplanes.
Contribution
It establishes the stability of solutions under hyperplane symmetries for the Logarithmic Minkowski problem, extending previous results to symmetric cases.
Findings
Stability is proven for solutions with hyperplane symmetries.
The results apply to the case of multiple independent hyperplanes.
The approach advances understanding of symmetric solutions in convex geometry.
Abstract
In the case of symmetries with respect to n independent linear hyperplanes, the stability of the solution of the Logarithmic Minkowski problem on S^{n-1} is established.
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Taxonomy
TopicsPoint processes and geometric inequalities · Geometric Analysis and Curvature Flows · Mathematical Inequalities and Applications