Hilbert metric, beyond convexity
Metric Geometry
2022-03-25 v1
Abstract
The Hilbert metric on convex subsets of 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.
Cite
@article{arxiv.1804.05317,
title = {Hilbert metric, beyond convexity},
author = {Elisha Falbel and Antonin Guilloux and Pierre Will},
journal= {arXiv preprint arXiv:1804.05317},
year = {2022}
}