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Finitude g\'eom\'etrique en g\'eom\'etrie de Hilbert + an erratum/addendum

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arxiv 1202.5442 v3 pith:A5JXATXN submitted 2012-02-24 math.GT math.GRmath.MG

Pierre-Louis Blayac (IRMA) , Mickaël Crampon , Ludovic Marquis (IRMAR) This is my paper · ORCID
classification math.GTmath.GRmath.MG
keywords arxiverratumhilbertaddendumetrieetriquefinitudepart
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The paper is divided in 2 parts. The first part is the original paper of the second and third authors arXiv:1202.5442v2. The second part is an erratum/addendum written in english and concatenated at the end of the former paper. In the erratum/addentum, we amend Theorems 1.3 and 1.11 of arXiv:1202.5442v2: Finitude g\'eom\'etrique en g\'eom\'etrie de Hilbert. We seize the opportunity to show that in round Hilbert geometry, geometrical finiteness (gf) is equivalent to cusp-uniform action and to fill some small gaps that appear in two other proofs of arXiv:1202.5442v2.

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  1. Transverse groups preserving proper domains in flag manifolds

    math.RT 2025-07 reject novelty 8.0 of 10

    Transverse groups preserving proper domains in flag manifolds must have limit triples of a single type (Maslov index zero in the tube-type case), but the proof of this key claim contains a false step.

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