Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimizing Neumann fundamental tones of triangles: an optimal Poincare
  inequality   The first nonzero eigenvalue of the Neumann Laplacian is shown to be minimal
for the degenerate acute isosceles triangle, among all triangles of given
diameter. Hence an optimal Poincar\'{e} inequality for triangles is derived.
  The proof relies on symmetry of the Neumann fundamental mode for isosceles
triangles with aperture less than $\pi/3$. Antisymmetry is proved for apertures
greater than $\pi/3$.

35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom