Volume entropy of Hilbert Geometries

  • Gautier Berck, Andreas Bernig, Constantin Vernicos
  • Published 2017


It is shown that among all plane Hilbert geometries, the hyperbolic plane has the maximal volume entropy. More precisely, it is shown that the volume entropy is bounded above by 2 3−d ≤ 1, where d is the Minkowski dimension of the extremal set of K. An explicit example of a plane Hilbert geometry with noninteger volume entropy is constructed. In arbitrary… (More)