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

Károly J. Böröczky; András Csépai; Ádám Sagmeister

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

Metric Geometry 2024-01-22 v2

Authors: Károly J. Böröczky , András Csépai , Ádám Sagmeister

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.

Keywords

hyperbolic space width functions bodies of constant width leichtweiss width characterization theorem

Cite

@article{arxiv.2303.16814,
  title  = {Hyperbolic width functions and characterizations of bodies of constant width in the hyperbolic space},
  author = {Károly J. Böröczky and András Csépai and Ádám Sagmeister},
  journal= {arXiv preprint arXiv:2303.16814},
  year   = {2024}
}

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19 pages, 4 figures

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

Abstract

Keywords

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