The Asymptotic Plateau Problem for $p$-Convex Hypersurfaces in Hyperbolic Space

We solve the asymptotic Plateau problem in hyperbolic space for the curvature given by the normalized geometric mean of the $p$-fold sums of the principal curvatures. For every $n\ge3$, $2\le p\le n-1$, and $σ\in(0,1)$, each bounded domain $Ω\subset\mathbb{R}^n$ with smooth mean-convex boundary admi