# Hilbert metric without convexity

Abstract : The Hilbert metric on convex subsets of $\mathbb R^n$ has proven a rich notion and has been extensively studied. We propose here a generalization of this metric to subset of complex projective spaces and give examples of applications to diverse fields. Basic examples include the classical Hilbert metric which coincides with the hyperbolic metric on real hyperbolic spaces as well as the complex hyperbolic metric on complex hyperbolic spaces.
Document type :
Journal articles
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https://hal.archives-ouvertes.fr/hal-01768400
Contributor : Antonin Guilloux Connect in order to contact the contributor
Submitted on : Tuesday, April 17, 2018 - 11:20:01 AM
Last modification on : Wednesday, September 28, 2022 - 3:06:08 PM

### Citation

Elisha Falbel, Antonin Guilloux, Pierre Will. Hilbert metric without convexity. Journal of Geometric Analysis, 2020, Gennadi Henkin: In Memoriam, 30, pp.2865-2896. ⟨10.1007/s12220-020-00426-x⟩. ⟨hal-01768400⟩

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