Extension of multivalued holomorphic functions on a Stein space

version of the classical Kerner’s theorem for a singular Stein space Ω with a compact strongly pseudoconvex boundary has been recently established by Huang–Xiao (J Reine Angew Math 770:183–203, 2021) when dim_ℂΩ≥ 3 . A partial result for the case of complex dimension two was also obtained in Huang and Xiao (J Reine Angew Math 770:183–203, 2021). In this paper, we answer the two dimensional case left open in Huang and Xiao (J Reine Angew Math 770:183–203, 2021) in its full generality.