Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The geometry of stable minimal surfaces in metric Lie groups   We study geometric properties of compact stable minimal surfaces with
boundary in homogeneous 3-manifolds $X$ that can be expressed as a semidirect
product of $\mathbb{R}^2$ with $\mathbb{R}$ endowed with a left invariant
metric. For any such compact minimal surface $M$, we provide a priori radius
estimate which depends only on the maximum distance of points of the boundary
$\partial M$ to a vertical geodesic of $X$. We also give a generalization of
the classical Rado's Theorem in $\mathbb{R}^3$ to the context of compact
minimal surfaces with graphical boundary over a convex horizontal domain in
$X$, and we study the geometry, existence and uniqueness of this type of
Plateau problem.

12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int