We prove that for any given upper semicontinuous function $varphi$ on an open subset $E$ of $mathbb C^nsetminus{0}$, such that the complex cone generated by $E$ minus the origin is connected, the homogeneous Siciak-Zaharyuta function with the weight
$varphi$ on $E$, can be represented as an envelope of a disc functional.
We construct a complete proper holomorphic embedding from any strictly pseudoconvex domain with $mathcal{C}^2$-boundary in $mathbb{C}^n$ into the unit ball of $mathbb{C}^N$, for $N$ large enough, thereby answering a question of Alarcon and Forstneric.
We provide a sufficient condition for open sets W and X such that a disc formula for the largest plurisubharmonic subextension of an upper semicontinuous function on a domain W to a complex manifold X holds.
The notion of the projective hull of a compact set in a complex projective space was introduced by Harvey and Lawson in 2006. In this paper we describe the projective hull by Poletsky sequences of analytic discs, in analogy to the known descriptions of the holomorphic and the plurisubharmonic hull.
