On Convex Projective Manifolds and Cusps
By Daryl Cooper, Darren D. Long, Stephan Tillmann. 2011
104 citations recorded by the source corpus.
This study of properly or strictly convex real projective manifolds introduces notions of parabolic, horosphere and cusp. Results include a Margulis lemma and in the strictly convex case a thick-thin decomposition. Finite volume cusps are shown to be projectively equivalent to cusps of hyperbolic manifolds. This is proved using a characterization of ellipsoids in projective space. Except in dimension 3, there are only finitely many topological types of strictly convex manifolds with bounded volume. In dimension 4 and higher, the diameter of a closed strictly convex manifold is at most 9 times the diameter of the thick part. There is an algebraic characterization of strict convexity in terms of relative hyperbolicity.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/94614d8c20f9ead0e6cb669257e988423b5690ba
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Around groups in Hilbert Geometry (2013, background): “The details can be found in [29] or [31]; the strategy is the same and can be traced back to the two-dimensional proof of [20].”