  In this paper, we solve the asymptotic Plateau problem in hyperbolic space
for constant $\sigma_{n-1}$ curvature, i.e. the existence of a complete
hypersurface in $\mathbb{H}^{n+1}$ satisfying $\sigma_{n-1}(\kappa)=\sigma\in
(0,n)$ with a prescribed asymptotic boundary $\Gamma$. The key ingredient is
the curvature estimates. Previously, this is only known for
$\sigma_0<\sigma<n$, where $\sigma_0$ is a positive constant.
