Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $(r,D,R)$-Blaschke-Santal\'o diagrams with regular $k$-gon gauges   We provide a study of Blaschke-Santal\'o diagrams for the inradius, diameter,
and circumradius, measured with respect to different gauges. This contrasts
previous works on those diagrams, which are all considered for euclidean
measure. By proving several new inequalities and properties between these three
functionals, we compute the intersection and the union over all possible gauges
of those diagrams, showing that they coincide with the corresponding diagrams
of a parallelotope and (in the planar case) a triangle, respectively. Further
new extremal properties are derived considering the diagrams with respect to a
regular pentagon or hexagon gauge.

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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat