Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space

Fernández, Isabel; Mira, Pablo

doi:10.1090/S0002-9947-09-04645-5

Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space
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by Isabel Fernández and Pablo Mira PDF

Trans. Amer. Math. Soc. 361 (2009), 5737-5752 Request permission

Abstract:

We classify the entire minimal vertical graphs in the Heisenberg group $\mathrm {Nil}_3$ endowed with a Riemannian left-invariant metric. This classification, which provides a solution to the Bernstein problem in $\mathrm {Nil}_3$, is given in terms of the Abresch-Rosenberg holomorphic differential for minimal surfaces in $\mathrm {Nil}_3$.

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