In this paper we apply the time dependent Ginzburg-Landau (TDGL) equations to the study of thin superconducting films of variable surfaces in the presence of an external applied magnetic field We have made a systematic investigation of both the lower and upper critical fields as a function of the topological parameters which control the shape of the film surfaces We also make a detailed investigation of the vortex dynamics as they nucleate into the sample. (C) 2009 Elsevier B V All rights reservedFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)