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In this article, we study the ramification of the Gauss map of completeminimal surfaces in R^3 and R^4 on annular ends. We obtain results which aresimilar to the ones obtained by Fujimoto and Ru for (the whole) completeminimal surfaces, thus we show that the restriction of the Gauss map to anannular end of such a complete minimal surface cannot have more branching (andin particular not avoid more values) than on the whole complete minimalsurface. We thus give an improvement of the results on annular ends of completeminimal surfaces of Kao.

Ramification of the Gauss Map of Complete Minimal Surfaces in R^3 and R^4 on Annular Ends