Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Optimal Plank Theorem   We give a new proof of Fejes T\'oth's zone conjecture: for any sequence
$v_1,v_2,...,v_n$ of unit vectors in a real Hilbert space $\mathcal{H}$, there
exists a unit vector $v$ in $\mathcal{H}$ such that \begin{equation*}
  |\langle v_k,v \rangle| \geq \sin(\pi/2n) \end{equation*} for all $k$. This
can be seen as sharp version of the plank theorem for real Hilbert spaces. Our
approach is inspired by Ball's solution to the complex plank problem and thus
unifies both the complex and the real solution under the same method.

19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin