On the Hilbert Geometry of products
classification
🧮 math.DG
math.MG
keywords
producthilbertamenabilityequivalentgeometryproveadditivebi-lipschitz
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We prove that the Hilbert geometry of a product of convex sets is bi-lipschitz equivalent the direct product of their respective Hilbert geometries. We also prove that the volume entropy is additive with respect to product and that amenability of a product is equivalent to the amenability of each terms.
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