Floating bodies for ball-convex bodies
Metric Geometry
2025-04-23 v1
Abstract
We define floating bodies in the class of -dimensional ball-convex bodies. A right derivative of volume of these floating bodies leads to a surface area measure for ball-convex bodies which we call relative affine surface area. We show that this quantity is a rigid motion invariant, upper semi continuous valuation.
Cite
@article{arxiv.2504.15488,
title = {Floating bodies for ball-convex bodies},
author = {Carsten Schuett and Elisabeth M Werner and Diliya Yalikun},
journal= {arXiv preprint arXiv:2504.15488},
year = {2025}
}