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Divisible convex sets with properly embedded cones
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DOI：10.1007/s10240-024-00152-y.png)
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Abstract
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In this article we construct many examples of properly convex irreducible domains divided by Zariski dense relatively hyperbolic groups in every dimension at least 3. This answers a question of Benoist. Relative hyperbolicity and non-strict convexity are captured by a family of properly embedded cones (convex hulls of points and ellipsoids) in the domain. Our construction is most flexible in dimension 3 where we give a purely topological criterion for the existence of a large deformation space of geometrically controlled convex projective structures with totally geodesic boundary on a compact 3-manifold.
Keywords:
PROJECTIVE-STRUCTURES
NONPOSITIVE CURVATURE
GEOMETRIC TRANSITION
MANIFOLDS
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