Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A variational characterization of calibrated submanifolds   Let $M$ be a fixed compact oriented embedded submanifold of a manifold
$\overline{M}$. Consider the volume $\mathcal{V} (\overline{g}) = \int_M
\mathsf{vol}_{(M, g)}$ as a functional of the ambient metric $\overline{g}$ on
$\overline{M}$, where $g = \overline{g}|_M$. We show that $\overline{g}$ is a
critical point of $\mathcal{V}$ with respect to a special class of variations
of $\overline{g}$, obtained by varying a calibration $\mu$ on $\overline{M}$ in
a particular way, if and only if $M$ is calibrated by $\mu$. We do not assume
that the calibration is closed. We prove this for almost complex, associative,
coassociative, and Cayley calibrations, generalizing earlier work of Arezzo-Sun
in the almost K\"ahler case. The Cayley case turns out to be particularly
interesting, as it behaves quite differently from the others. We also apply
these results to obtain a variational characterization of Smith maps.

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The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph