An Extension of the Affine Bernstein Problem
2011 - J.A. Aledo, A. Martínez y F. Milán
Results in Mathematics 60 (2011), 157--174.
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.