2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172676In the previous paper, the authors constructed a complete holomorphic immersion of the unit disk D into C^2 whose image is bounded. In this paper, we shall prove existence of complete holomorphic null immersions of Riemann surfaces with arbitrary genus and finite topology, whose image is bounded in C^2. To construct such immersions, we apply the method used by F. J. Lopez to perturb the genus zero example changing its genus. As an analogue the above construction, we also give a new method to construct complete bounded minimal immersions (resp. weakly complete maximal surface) with arbitrary genus and finite topology in Euclidean 3-space (resp. Lorentz-Minkowski 3-spacetime).12 pages, 1 figureDifferential Geometry53A10; 49Q05text