Year: 2023
Type: preprint
Abstract: In convex geometry, the constructions that assign to a convex body its difference body, projection body, or volume have the following properties: They are (1) invariant under volume-preserving linear changes of coordinates; (2) continuous; (3) finitely additive, and the resulting convex bodies are subsets of an irreducible representation of the special linear group. In this paper we explore the question whether there exist other constructions with these properties. We discover a surprising dichotomy: There are no new examples if one assumes translation invariance, but a plethora of examples without this assumption.
Source: arXiv (Cornell University)
Authors: Henkel, Jakob, Wannerer, Thomas
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G748164020
OpenAlex ID: W4367190850