Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the second variation of the Graham-Witten energy   The area renormalization procedure gives an invariant of even-dimensional
closed submanifolds in a conformal manifold, which we call the Graham-Witten
energy, and it is a generalization of the classical Willmore energy. In this
paper, we obtain an explicit formula for the second variation of this energy at
minimal submanifolds in an Einstein manifold. As an application, we prove that
the even-dimensional totally geodesic spheres in the unit sphere are critical
points of the Graham-Witten energy with non-negative second variation.

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The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: eess