Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 3-Manifolds with Yamabe invariant greater than that of $\RP^3$   We complete the classification (started by Bray and the second author) of all
closed 3-manifolds with Yamabe invariant greater than that of $\RP^3$, by
showing that such manifolds are either $S^3$ or finite connected sums $# m(S^2
\times S^1) # n(S^2 \tilde{\times} S^1)$ for $m + n \geq 1$, where $S^2
\tilde{\times} S^1$ is the nonorientable $S^2$-bundle over $S^1$.
  A key ingredient is Aubin's Lemma, which says that if the Yamabe constant is
positive, then it is strictly less than the Yamabe constant of any of its
non-trivial finite conformal coverings. This lemma, combined with inverse mean
curvature flow and with analysis of the Green's functions for the conformal
Laplacians on specific finite and normal infinite Riemannian coverings, will
allow us to construct a family of nice test functions on the finite coverings
and thus prove the desired result.

33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs