Trees and ultrametric Möbius structures

Abstract

We define the concept of an ultrametric Möbius space (Z,M) and show that the boundary at infinity of a nonelementary geodesically complete tree is naturally an ultrametric Möbius space. In addition, we construct to a given ultrametric Möbius space (Z,M) a nonelementary geodesically complete tree, unique up to isometry, with (Z,M) being its boundary at infinity. This yields a one-to-one correspondence.

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Correspondence to Jonas Beyrer.

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The text was submitted by the authors in English.

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Beyrer, J., Schroeder, V. Trees and ultrametric Möbius structures. P-Adic Num Ultrametr Anal Appl 9, 247–256 (2017). https://doi.org/10.1134/S207004661704001X

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Key words

  • trees
  • Möbius structures
  • ultrametrics