Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Translating solitons in Riemannian products   In this paper we study solitons invariant with respect to the flow generated
by a complete Killing vector field in a ambient Riemannian manifold. A special
case occurs when the ambient manifold is the Riemannian product $(\mathbb{R}
\times P, {\rm d}t^2+g_0)$ and the Killing field is $X=\partial_t$. Similarly
to what happens in the Euclidean setting, we call them translating solitons. We
see that a translating soliton in $\mathbb{R} \times P$ can be seen as a
minimal submanifold for a weighted volume functional. Moreover we show that
this kind of solitons appear in a natural way in the context of a monotonicity
formula for the mean curvature flow in $\mathbb{R} \times P$. When $g_0$ is
rotationally invariant and its sectional curvature is non-positive, we are able
to characterize all the rotationally invariant translating solitons.
Furthermore, we use these families of new examples as barriers to deduce
several non-existence results.

33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph