The geometry of convex affine maximal graphs (Q2774473)

It is well-known that the affine analogue of Bernstein's problem in 3-space has the following solution: Every affinely complete affine minimal graph \((x,y,f (x,y))\) over \(R^2\) with definitie affine metric tensor is affinely equivalent to the elliptic paraboloid \(f(x,y)= x^2+y^2\). The authors extend this theorem to Euclidean complete affine minimal surfaces with a so-called ``regular-balanced'' annular end applying the classical Jörgens' theorem [\textit{K. Jörgens}, Math. Ann. 127, 130-134 (1954; Zbl 0055.08404)]. Moreover, by function theoretical methods they obtain an explicit representation of the end of an arbitrary affine minimal surface with a regular-balanced end after using its tangent improper affine sphere at infinity.