Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the role of curvature in the elastic energy of non-Euclidean thin
  bodies   We prove a relation between the scaling $h^\beta$ of the elastic energies of
shrinking non-Euclidean bodies $S_h$ of thickness $h\to 0$, and the curvature
along their mid-surface $S$. This extends and generalizes similar results for
plates [BLS16, LRR] to any dimension and co-dimension. In particular, it proves
that the natural scaling for non-Euclidean rods with smooth metric is $h^4$, as
claimed in [AAE+12] using a formal asymptotic expansion. The proof involves
calculating the $\Gamma$-limit for the elastic energies of small balls
$B_h(p)$, scaled by $h^4$, and showing that the limit infimum energy is given
by a square of a norm of the curvature at a point $p$. This $\Gamma$-limit
proves asymptotics calculated in [AKM+16].

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The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph