Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity Theorems for Asymptotically Euclidean $Q$-singular Spaces   In this paper we prove some rigidity theorems associated to $Q$-curvature
analysis on asymptotically Euclidean (AE) manifolds, which are inspired by the
analysis of conservation principles within fourth order gravitational theories.
A central object in this analysis is a notion of fourth order energy,
previously analysed by the authors, which is subject to a positive energy
theorem. We show that this energy can be more geometrically rewritten in terms
of a fourth order analogue to the Ricci tensor, which we denote by $J_g$. This
allows us to prove that Yamabe positive $J$-flat AE manifolds must be isometric
to Euclidean space. As a by product, we prove that this $J$-tensor provides a
geometric control for the optimal decay rates at infinity. This last result
reinforces the analogy of $J$ as a fourth order analogue to the Ricci tensor.

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The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: econ
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
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The categories of this paper are: eess
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg