Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unique continuation from infinity in asymptotically Anti-de Sitter
  spacetimes   We consider the unique continuation properties of asymptotically Anti-de
Sitter spacetimes by studying Klein-Gordon-type equations $\Box_g \phi + \sigma
\phi = \mathcal{G} ( \phi, \partial \phi )$, $\sigma \in \mathbb{R}$, on a
large class of such spacetimes. Our main result establishes that if $\phi$
vanishes to sufficiently high order (depending on $\sigma$) on a sufficiently
long time interval along the conformal boundary $\mathcal{I}$, then the
solution necessarily vanishes in a neighborhood of $\mathcal{I}$. In
particular, in the $\sigma$-range where Dirichlet and Neumann conditions are
possible on $\mathcal{I}$ for the forward problem, we prove uniqueness if both
these conditions are imposed. The length of the time interval can be related to
the refocusing time of null geodesics on these backgrounds and is expected to
be sharp. Some global applications as well a uniqueness result for
gravitational perturbations are also discussed. The proof is based on novel
Carleman estimates established in this setting.

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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con