On the entropy of Hilbert geometries of low regularities

DOI10.1007/s10711-023-00828-5zbMath1522.51011arXiv1612.02974OpenAlexW2565878965MaRDI QIDQ6093594

Louis Merlin, Jan Cristina

Publication date: 7 September 2023

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.02974

zbMATH Keywords

Sobolev spacesCantor setgeometric measure theoryFinslerian geometryHilbert geometryvolume entropyAhlfors regularity

Mathematics Subject Classification ID

Metric geometry (51F99) Length, area, volume, other geometric measure theory (28A75) Fractals (28A80) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60)

Cites Work

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• Handbook of Hilbert geometry
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• Hilbert geometry for strictly convex domains
• Entropy and rigidity of locally symmetric spaces of strictly negative curvature
• On the second differentiability of convex surfaces
• Volume entropy of Hilbert metrics and length spectrum of Hitchin representations into \(\mathrm{PSL}(3,\mathbb{R})\)
• The Ptolemaic inequality in Hilbert geometries
• Intrinsic area
• Ahlfors-David regular sets and bilipschitz maps
• Quasiconformal Mappings and Royden Algebras in Space

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