A proper metric space quasi-isometric to a finitely generated group and a horoball space over such a group must be quasi-isometric to a rank-one symmetric space or the real line.
Convergence groups and S eifert fibered 3 -manifolds
2 Pith papers cite this work. Polarity classification is still indexing.
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In FPP on hyperbolic groups, the set of exceptional directions has strictly smaller Hausdorff dimension than the boundary and exists densely with multiple disjoint geodesics when boundary dimension exceeds one.
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Hyperbolic spaces with geometric and geometrically finite quasi-actions are symmetric
A proper metric space quasi-isometric to a finitely generated group and a horoball space over such a group must be quasi-isometric to a rank-one symmetric space or the real line.
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Geodesic Trees and Exceptional Directions in FPP on Hyperbolic Groups
In FPP on hyperbolic groups, the set of exceptional directions has strictly smaller Hausdorff dimension than the boundary and exists densely with multiple disjoint geodesics when boundary dimension exceeds one.