Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremizers for Adjoint Restriction to a Pair of Reflected Paraboloids   We consider the adjoint restriction inequality associated to the hypersurface
$\{(\tau, \xi) : \tau = \pm|\xi|^2, \;\xi \in \mathbb{R}^d\}$ at the
Stein-Tomas exponent. Extremizers exist in all dimensions and extremizing
sequences are precompact modulo symmetries conditional on a certain inequality,
which we verify in the case $d \in \{1,2\}$.

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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con