English

On the entropy of Hilbert Geometries of Low Regularities

Metric Geometry 2020-01-10 v2

Abstract

We compare the regularity of the boundary of a convex set with the value of its Finslerian volume entropy. The main result states that the volume entropy of a two-dimensional domain whose associated curvature measure is Ahlfors α\alpha-regular is 2αα+1\frac{2\alpha}{\alpha +1}.

Keywords

Cite

@article{arxiv.1612.02974,
  title  = {On the entropy of Hilbert Geometries of Low Regularities},
  author = {Jan Cristina and Louis Merlin},
  journal= {arXiv preprint arXiv:1612.02974},
  year   = {2020}
}

Comments

Complete rewriting