Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space

By I. Fernández, Pablo Mira. 2007

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We classify the entire minimal vertical graphs in the Heisenberg group Nil 3 endowed with a Riemannian left-invariant metric. This classification, which provides a solution to the Bernstein problem in Nil 3 , is given in terms of the Abresch-Rosenberg holomorphic differential for minimal surfaces in Nil 3 .

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f96f5ca5e5bdfc56e7cb956b668fb0efe94ec438