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In this work we study a class of affine maximal surfaces with singularities that we call affine maximal maps. Our main goal is the classification of the complete affine maximal maps with one or two embedded regular ends. In particular, we obtain a new characterization of the elliptic paraboloid and a large family of global examples.
.The paper deals with the study of affine maximal surfaces with admissible singularities. We shall give some fundamental notions, results, tools and open problems that keep unsolved up to date.
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