Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spacelike convex surfaces with prescribed curvature in (2+1)-Minkowski
  space   We prove existence and uniqueness of solutions to the Minkowski problem in
any domain of dependence $D$ in $(2+1)$-dimensional Minkowski space, provided
$D$ is contained in the future cone over a point. Namely, it is possible to
find a smooth convex Cauchy surface with prescribed curvature function on the
image of the Gauss map. This is related to solutions of the Monge-Amp\`ere
equation $\det D^2 u(z)=(1/\psi(z))(1-|z|^2)^{-2}$ on the unit disc, with the
boundary condition $u|_{\partial\mathbb{D}}=\varphi$, for $\psi$ a smooth
positive function and $\varphi$ a bounded lower semicontinuous function.
  We then prove that a domain of dependence $D$ contains a convex Cauchy
surface with principal curvatures bounded from below by a positive constant if
and only if the corresponding function $\varphi$ is in the Zygmund class.
Moreover in this case the surface of constant curvature $K$ contained in $D$
has bounded principal curvatures, for every $K<0$. In this way we get a full
classification of isometric immersions of the hyperbolic plane in Minkowski
space with bounded shape operator in terms of Zygmund functions of $\partial
\mathbb{D}$.
  Finally, we prove that every domain of dependence as in the hypothesis of the
Minkowski problem is foliated by the surfaces of constant curvature $K$, as $K$
varies in $(-\infty,0)$.

36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci