Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Total curvature and spiralling shortest paths   This paper gives a partial confirmation of a conjecture of P. Agarwal, S.
Har-Peled, M. Sharir, and K. Varadarajan that the total curvature of a shortest
path on the boundary of a convex polyhedron in the 3-dimensional Euclidean
space cannot be arbitrarily large. It is shown here that the conjecture holds
for a class of polytopes for which the ratio of the radii of the circumscribed
and inscribed ball is bounded. On the other hand, an example is constructed to
show that the total curvature of a shortest path on the boundary of a convex
polyhedron can exceed 2 \pi. Another example shows that the spiraling number of
a shortest path on the boundary of a convex polyhedron can be arbitrarily
large.

11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat