On Lipschitz compactifications of trees

Benoît Kloeckner

doi:10.1016/j.crma.2008.02.011

Geometry

On Lipschitz compactifications of trees

Presented by: Étienne Ghys

Benoît Kloeckner ¹

¹ Institut Fourier, université de Grenoble I, UMR 5582 CNRS–UJF, 38402 St Martin d'Hères, France

Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 413-416.

Abstract
Résumé

We study the Lipschitz structures on the geodesic compactification of a regular tree, that are preserved by the automorphism group. They are shown to be similar to the compactifications introduced by William Floyd, and a complete description is given.

On étudie les structures lipschitziennes portées par la compactification géodésique d'un arbre régulier, et qui sont préservées par l'action du groupe des automorphismes. On montre qu'elles sont semblables aux compactifications définies par William Floyd, et on en donne une description complète.

Received: 2008-01-25
Accepted: 2008-02-09
Published online: 2008-03-03

DOI: 10.1016/j.crma.2008.02.011

Author's affiliations:

Benoît Kloeckner ¹

¹ Institut Fourier, université de Grenoble I, UMR 5582 CNRS–UJF, 38402 St Martin d'Hères, France

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     title = {On {Lipschitz} compactifications of trees},
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Benoît Kloeckner. On Lipschitz compactifications of trees. Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 413-416. doi : 10.1016/j.crma.2008.02.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.02.011/

References
Cited by

[1] M. Bourdon Immeubles hyperboliques, dimension conforme et rigidité de Mostow, Geom. Funct. Anal., Volume 7 (1997) no. 2, pp. 245-268

[2] D. Burago; Y. Burago; S. Ivanov A Course in Metric Geometry, Graduate Studies in Mathematics, vol. 33, American Mathematical Society, Providence, RI, 2001

[3] W.J. Floyd Group completions and limit sets of Kleinian groups, Invent. Math., Volume 57 (1980) no. 3, pp. 205-218

[4] B. Kloeckner On differentiable compactifications of the hyperbolic space, Transform. Groups, Volume 11 (2006) no. 2, pp. 185-194

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