Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational Properties Of The Second Eigenvalue Of The Conformal
  Laplacian   Let $(M^n,g)$ be a closed Riemannian manifold of dimension $n\ge 3$. Assume
$[g]$ is a conformal class for which the Conformal Laplacian $L_g$ has at least
two negative eigenvalues. We show the existence of a (generalized) metric that
maximizes the second eigenvalue of $L_g$ over all conformal metrics (the first
eigenvalue is maximized by the Yamabe metric). We also show that a maximal
metric defines either a nodal solution of the Yamabe equation, or a harmonic
map to a sphere. Moreover, we construct examples of each possibility.

10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci