2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119121Walter Rudin, in 1966, characterized analytic functions in the unit disk in terms of the maximum principle relative to the boundary. We conjecture a generalization of this result when the disk is replaced by the punctured disk, and we prove a special case of this conjecture, making use of the notion of projective hull in P^n introduced by R. Harvey and B. Lawson.Complex Variables30H05, 32A38, 46J15, 46E25text