Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence theorems of the fractional Yamabe problem   Let $X$ be an asymptotically hyperbolic manifold and $M$ its conformal
infinity. This paper is devoted to deduce several existence results of the
fractional Yamabe problem on $M$ under various geometric assumptions on $X$ and
$M$: Firstly, we handle when the boundary $M$ has a point at which the mean
curvature is negative. Secondly, we re-encounter the case when $M$ has zero
mean curvature and is either non-umbilic or umbilic but non-locally conformally
flat. As a result, we replace the geometric restrictions given by
Gonz\'alez-Qing (Analysis and PDE, 2013) and Gonz\'alez-Wang (arXiv:1503.02862)
with simpler ones. Also, inspired by Marques (Comm. Anal. Geom., 2007) and
Almaraz (Pacific J. Math., 2010), we study lower-dimensional manifolds.
Finally, the situation when $X$ is Poincar\'e-Einstein, $M$ is either locally
conformally flat or 2-dimensional is covered under the validity of the positive
mass theorem for the fractional conformal Laplacians.

27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg