Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Concentration for SU(1,1) Coherent State Transforms and an
  analogue of the Lieb-Wehrl Conjecture for SU(1,1)   We derive a lower bound for the Wehrl entropy in the setting of SU(1,1). For
asymptotically high values of the quantum number k, this bound coincides with
the analogue of the Lieb-Wehrl conjecture for SU(1,1) coherent states. The
bound on the entropy is proved via a sharp norm bound. The norm bound is
deduced by using an interesting identity for Fisher information of SU(1,1)
coherent state transforms and a new family of sharp Sobolev inequalities on the
hyperbolic plane. To prove the sharpness of our Sobolev inequality, we need to
first prove a uniqueness theorem for solutions of a semi-linear Poisson
equation (which is actually the Euler-Lagrange equation for the variational
problem associated with our sharp Sobolev inequality) on the hyperbolic plane.
Uniqueness theorems proved for similar semi-linear equations in the past do not
apply here and the new features of our proof are of independent interest, as
are some of the consequences we derive from the new family of Sobolev
inequalities.

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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
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The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg