Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global maximizers for adjoint Fourier restriction inequalities on low
  dimensional spheres   We prove that constant functions are the unique real-valued maximizers for
all $L^2-L^{2n}$ adjoint Fourier restriction inequalities on the unit sphere
$\mathbb{S}^{d-1}\subset\mathbb{R}^d$, $d\in\{3,4,5,6,7\}$, where $n\geq 3$ is
an integer. The proof uses tools from probability theory, Lie theory,
functional analysis, and the theory of special functions. It also relies on
general solutions of the underlying Euler-Lagrange equation being smooth, a
fact of independent interest which we establish in a companion paper. We
further show that complex-valued maximizers coincide with nonnegative
maximizers multiplied by the character $e^{i\xi\cdot\omega}$, for some $\xi$,
thereby extending previous work of Christ & Shao to arbitrary dimensions $d\geq
2$ and general even exponents.

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The categories of this paper are: eess
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The categories of this paper are: nlin
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc