Corpus ID: 235421722

The boundary of rank-one divisible convex sets

@inproceedings{Blayac2021TheBO,
title={The boundary of rank-one divisible convex sets},
author={Pierre-Louis Blayac},
year={2021}
}
We prove that for any non-symmetric irreducible divisible convex set, the proximal limit set is the full projective boundary.
2 Citations

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References

SHOWING 1-10 OF 31 REFERENCES
A higher rank rigidity theorem for convex real projective manifolds
For convex real projective manifolds we prove an analogue of the higher rank rigidity theorem of Ballmann and Burns-Spatzier.
Codimension-$1$ Simplices in Divisible Convex Domains
Properly embedded simplices in a convex divisible domain $\Omega \subset \mathbb{R} \textrm{P}^d$ behave somewhat like flats in Riemannian manifolds, so we call them flats. We show that the set ofExpand
Manifolds of nonpositive curvature and their buildings
• Mathematics
• 1987
AbstractLet M be a complete Riemannian manifold of bounded nonpositive sectional curvature and finite volume. We construct a topological Tits building Δ $$\tilde M$$ associated to the universalExpand
Convex co-compact actions of relatively hyperbolic groups.
• Mathematics
• 2019
In this paper we consider discrete groups in ${\rm PGL}_d(\mathbb{R})$ acting convex co-compactly on a properly convex domain in real projective space. For such groups, we establish necessary andExpand
Patterson--Sullivan densities in convex projective geometry
For any rank-one convex projective manifold with a compact convex core, we prove that there exists a unique probability measure of maximal entropy on the set of unit tangent vectors whose geodesic isExpand
The Minnesota Notes on Jordan Algebras and Their Applications
• Mathematics
• 1999
Domains of Positivity.- Omega Domains.- Jordan Algebras.- Real and Complex Jordan Algebras.- Complex Jordan Algebras.- Jordan Algebras and Omega Domains.- Half-Spaces.- Appendix: The Bergman kernelExpand
Propriétés Asymptotiques des Groupes Linéaires
Abstract. Let G be a reductive linear real Lie group and $\Gamma$ be a Zariski dense subgroup. We study asymptotic properties of $\Gamma$ through the set of logarithms of the radial components ofExpand
Geometry, Analysis and Topology of Discrete Groups
This new volume presents 15 papers treating discrete groups as they occur in areas such as algebra, analysis, geometry, number theory and topology. Most of the papers are surveys, and the volume isExpand
Sur les automorphismes affines des ouverts convexes saillants
© Scuola Normale Superiore, Pisa, 1970, tous droits réservés. L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze »Expand
Sur les variétés localement affines et localement projectives
© Bulletin de la S. M. F., 1960, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html) implique l’accordExpand