Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A norm - inequality related to affine regular hexagons   Let $(E, \lVert . \rVert)$ be a two-dimensional real normed space with unit
sphere $S = \{x \in E, \lVert x \rVert = 1\}$. The main result of this paper is
the following: Consider an affine regular hexagon with vertex set $H = \{\pm
v_1, \pm v_2, \pm v_3\} \subseteq S$ inscribed to $S$. Then we have $$\min_i
\max_{x \in S}{\lVert x - v_i \rVert + \lVert x + v_i \rVert} \leq 3.$$ From
this result we obtain $$\min_{y \in S} \max_{x \in S}{\lVert x - y \rVert +
\lVert x + y \rVert} \leq 3,$$ and equality if and only if $S$ is a
parallelogram or an affine regular hexagon.

9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th