On the entropy of Hilbert Geometries of Low Regularities
  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 $\alpha$-regular is $\frac{2\alpha}{\alpha +1}$. 
Jan Cristina and Louis Merlin
math.MG