Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Piecewise Flat Extrinsic Curvature   Discretizations of the mean curvature and extrinsic curvature components are
constructed on piecewise flat simplicial manifolds, giving approximations for
smooth curvature values in a mostly mesh-independent way. These constructions
are given in combinatoric form in terms of the extrinsic hinge angles, the
intrinsic structure of the piecewise flat manifold and a choice of dual
tessellation, and can be viewed as the average of $n$-volume integrals. The
constructions are also independent of the manifold dimension.

3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
14
The categories of this paper are: math-ph