Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Line transversals to disjoint balls   We prove that the set of directions of lines intersecting three disjoint
balls in $R^3$ in a given order is a strictly convex subset of $S^2$. We then
generalize this result to $n$ disjoint balls in $R^d$. As a consequence, we can
improve upon several old and new results on line transversals to disjoint balls
in arbitrary dimension, such as bounds on the number of connected components
and Helly-type theorems.

32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
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The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom