Maximal radius of quaternionic hyperbolic manifolds

Zoé Philippe

doi:10.5802/afst.1586

Zoé Philippe ¹

¹ missing address

Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 27 (2018) no. 5, pp. 875-896.

Abstract
Abstract

We derive an explicit lower bound on the radius of a ball embedded in a quaternionic hyperbolic manifold (the maximal radius). We then deduce a lower bound on the volume of a quaternionic hyperbolic manifold. Both those bounds decrease with the dimension, when it is not clear that it should be the behaviour of the maximal radius or of the minimal volume. Related to that question, we note however that the Margulis constant of the quaternionic hyperbolic space of dimension $n$ is smaller than $C / \sqrt{n}$ , so is decreasing as the dimension grows.

Nous donnons une borne inférieure explicite sur le rayon d’une boule plongée dans une variété hyperbolique quaternionique (le rayon maximal). Nous en déduisons une minoration du volume de telles variétés. Les deux bornes exhibées décroissent avec la dimension, et il n’est pas clair que l’on doive s’attendre au même comportement pour le rayon maximal ou pour le volume minimal. En lien avec cette question, nous remarquons cependant que la constante de Margulis de l’espace hyperbolique quaternionique de dimension $n$ est inférieure à $C / \sqrt{n}$ , et décroit donc quand la dimension augmente.

Received: 2015-09-21
Accepted: 2015-10-14
Published online: 2019-01-21

MR Zbl

DOI: 10.5802/afst.1586

Author's affiliations:

Zoé Philippe ¹

¹ missing address

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Zo\'e Philippe},
     title = {Maximal radius of quaternionic hyperbolic manifolds},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {875--896},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 27},
     number = {5},
     year = {2018},
     doi = {10.5802/afst.1586},
     zbl = {1412.53073},
     mrnumber = {3919543},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1586/}
}

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Zoé Philippe. Maximal radius of quaternionic hyperbolic manifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 27 (2018) no. 5, pp. 875-896. doi : 10.5802/afst.1586. https://afst.centre-mersenne.org/articles/10.5802/afst.1586/

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