Local fixed point results for centroid body operators
Metric Geometry
2024-08-27 v2
Abstract
We prove that, in a neighborhood of the Euclidean ball, there are no other fixed points of the -centroid body operator, using spherical harmonic techniques. We also show that the Euclidean ball is locally the only body whose centroid body is a dilate of its polar intersection body.
Cite
@article{arxiv.2312.10574,
title = {Local fixed point results for centroid body operators},
author = {Chase Reuter},
journal= {arXiv preprint arXiv:2312.10574},
year = {2024}
}