Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Piecewise flat Ricci flow of compact without boundary three-manifolds   Using a recently developed piecewise flat method, numerical evolutions of the
Ricci flow are computed for a number of manifolds, using a number of different
mesh types, and shown to converge to the expected smooth behaviour as the mesh
resolution is increased. The manifolds were chosen to have varying degrees of
homogeneity, and include Nil and Gowdy manifolds, a three-torus initially
embedded in Euclidean four-space, and a perturbation of a flat three-torus. The
piecewise flat Ricci flow of the first two are shown to converge to analytic
and numerical partial differential equation solutions respectively, with the
remaining two flowing asymptotically to flat metrics.

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The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
18
The categories of this paper are: econ