Hilbert-geometry covering numbers satisfy polarity duality: N^H_K(G, α) is bounded above and below by c^{±d} times N^H_{G°}(K°, α) for an absolute constant c.
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2 Pith papers cite this work. Polarity classification is still indexing.
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An analog of Cauchy's surface area formula is established for Funk geometry on a convex body K using Holmes-Thompson area and central projections, reducing to a weighted vertex sum for polytopes and yielding a generalized Crofton formula.
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On the Duality of Coverings in Hilbert Geometry
Hilbert-geometry covering numbers satisfy polarity duality: N^H_K(G, α) is bounded above and below by c^{±d} times N^H_{G°}(K°, α) for an absolute constant c.
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Cauchy's Surface Area Formula in the Funk Geometry
An analog of Cauchy's surface area formula is established for Funk geometry on a convex body K using Holmes-Thompson area and central projections, reducing to a weighted vertex sum for polytopes and yielding a generalized Crofton formula.