Hartogs extension (codim-2 singularities auto-extend for n ≥ 2)

Hartogs 1906 (Math. Ann. 62). For n ≥ 2, a holomorphic function on the Hartogs figure H_{n,ε} = {z : |z₁| < 1, |z_j| < ε for j ≥ 2} ∪ {z : |z₁| < ε, |z_j| < 1 for j ≥ 2} extends uniquely to the full polydisk D^n. Equivalently:…