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Journal Articles Journal of Geometric Analysis Year : 2020

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.

Dates and versions

hal-01768400 , version 1 (17-04-2018)

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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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