Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space

Fernández, Isabel; Mira, Pablo

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

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ISSN 1088-6850(online) ISSN 0002-9947(print)

Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space

Authors: Isabel Fernández and Pablo Mira
Journal: Trans. Amer. Math. Soc. 361 (2009), 5737-5752
MSC (2000): Primary 53A10
Posted: June 22, 2009
MathSciNet review: 2529912
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Abstract: We classify the entire minimal vertical graphs in the Heisenberg group ${\rm Nil_3}$ endowed with a Riemannian left-invariant metric. This classification, which provides a solution to the Bernstein problem in ${\rm Nil}_3$ , is given in terms of the Abresch-Rosenberg holomorphic differential for minimal surfaces in ${\rm Nil}_3$ .

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