Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blocking: New examples and properties of products   We say that a pair of points x and y is secure if there exist a finite set of
blocking points such that any geodesic between x and y passes through one of
the blocking points. The main point of this paper is to exhibit new examples of
blocking phenomena both in the manifold and the billiard table setting. As an
approach to this, we study if the product of secure configurations (or
manifolds) is also secure.
  We introduce the concept of midpoint security that imposes that the geodesic
reaches a blocking point exactly at its midpoint. We prove that products of
midpoint secure configurations are midpoint secure. On the other hand, we give
an example of a compact C^1 surface that contains secure configurations that
are not midpoint secure. This surface provides the first example of an insecure
product of secure configurations, as well as billiard table examples.

17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc