Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Crystalline Order On Riemannian Manifolds With Variable Gaussian
  Curvature And Boundary   We investigate the zero temperature structure of a crystalline monolayer
constrained to lie on a two-dimensional Riemannian manifold with variable
Gaussian curvature and boundary. A full analytical treatment is presented for
the case of a paraboloid of revolution. Using the geometrical theory of
topological defects in a continuum elastic background we find that the presence
of a variable Gaussian curvature, combined with the additional constraint of a
boundary, gives rise to a rich variety of phenomena beyond that known for
spherical crystals. We also provide a numerical analysis of a system of
classical particles interacting via a Coulomb potential on the surface of a
paraboloid.

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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci