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- W1977029685 abstract "It is shown that the volume entropy of a Hilbert geometry associated to an $n$-dimensional convex body of class $C^{1,1}$ equals $n-1$. To achieve this result, a new projective invariant of convex bodies, similar to the centro-affine area, is constructed. In the case $n=2$, and without any assumption on the boundary, it is shown that the entropy is bounded above by $frac{2}{3-d} leq 1$, where $d$ is the Minkowski dimension of the extremal set of $K$. An example of a plane Hilbert geometry with entropy strictly between 0 and 1 is constructed." @default.
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- W1977029685 date "2008-10-07" @default.
- W1977029685 modified "2023-09-27" @default.
- W1977029685 title "Volume entropy of Hilbert Geometries" @default.
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