Hyperbolic width functions and characterizations of bodies of constant width in the hyperbolic space

Abstract

We discuss basic properties of several different width functions in the $n$-dimensional hyperbolic space such as continuity, and we also define a new hyperbolic width as the extension of Leichtweiss' width function. Then we prove a characterization theorem of bodies of constant width regarding the aforementioned notions of hyperbolic width.

19 pages, 4 figures