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PreprintarXiv licencearXiv

Möbius Maps, Reflections and Lipschitz Constants

  • Alan F. Beardon
  • Toshiyuki Sugawa
  • Matti Vuorinen
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Abstract

We introduce the chordal isometric circle of a Möbius map, and use this to give a factorization of any Möbius map as the composition of a chordal isometry and either a reflection, or a rotary reflection, across a circle. We then use this to find the chordal, and spherical, Lipschitz constants of a Möbius map, and compare this with related results in the literature.

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Cite

BibTeXRIS
BibTeX
@misc{beardon2026möbius,
  title = {{Möbius Maps, Reflections and Lipschitz Constants}},
  author = {Alan F. Beardon and Toshiyuki Sugawa and Matti Vuorinen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25644},
  eprint = {2609.25644},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25644},
}
RIS
TY  - UNPB
TI  - Möbius Maps, Reflections and Lipschitz Constants
AU  - Alan F. Beardon
AU  - Toshiyuki Sugawa
AU  - Matti Vuorinen
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.25644
UR  - https://arxiv.org/abs/2609.25644
AB  - We introduce the chordal isometric circle of a Möbius map, and use this to give a factorization of any Möbius map as the composition of a chordal isometry and either a reflection, or a rotary reflection, across a circle. We then use this to find the chordal, and spherical, Lipschitz constants of a Möbius map, and compare this with related results in the literature.
ER  -