Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and uniqueness of solutions to the constant mean curvature
  equation with nonzero Neumann boundary data in product manifold
  $M^{n}\times\mathbb{R}$   In this paper, we can prove the existence and uniqueness of solutions to the
constant mean curvature (CMC for short) equation with nonzero Neumann boundary
data in product manifold $M^{n}\times\mathbb{R}$, where $M^{n}$ is an
$n$-dimensional ($n\geq2$) complete Riemannian manifold with nonnegative Ricci
curvature, and $\mathbb{R}$ is the Euclidean $1$-space. Equivalently, this
conclusion gives the existence of CMC graphic hypersurfaces defined over a
compact strictly convex domain $\Omega\subset M^{n}$ and having arbitrary
contact angle.

24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn