Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space
Abstract
Description
We classify the entire minimal vertical graphs in the 3 dimensional Heisenberg group Nil endowed with a Riemannian left-invariant metric. This classification, which provides a solution to the Bernstein problem in Nil, is given in terms of the Abresch-Rosenberg holomorphic differential for minimal surfaces in Nil.
17 pages, 1 figure, revised version
17 pages, 1 figure, revised version