On the entropy of Hilbert Geometries of Low Regularities

2016/12/09 by Jan Cristina, Cristina, Jan, Louis Merlin +1
Mathematics · Physics and Astronomy · #28A75 #28A80 #51F99 #51M10 #53C60 #Advanced Differential Geometry Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations #math.MG #msc:28A75 #msc:28A80 #msc:51F99 #msc:51M10 #msc:53C60

paper · pdf · doi:10.48550/arxiv.1612.02974

Complete rewriting

openalex publication_date 2016/12/09 · arxiv created 2020/01/09 · arxiv updated 2020/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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-regular is (2α)/(α+1).

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