Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimization of the lowest eigenvalue for leaky star graphs   We consider the problem of geometric optimization for the lowest eigenvalue
of the two-dimensional Schr\"odinger operator with an attractive
$\delta$-interaction of a fixed strength, the support of which is a star graph
with finitely many edges of an equal length $L \in (0,\infty]$. Under the
constraint of fixed number of the edges and fixed length of them, we prove that
the lowest eigenvalue is maximized by the fully symmetric star graph. The proof
relies on the Birman-Schwinger principle, properties of the Macdonald function,
and on a geometric inequality for polygons circumscribed into the unit circle.

17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio