## 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 $\mathrm {Nil}_3$.## References

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## Additional Information

**Isabel Fernández**- Affiliation: Departamento de Matematica Aplicada I, Universidad de Sevilla, E-41012 Sevilla, Spain
- Email: isafer@us.es
**Pablo Mira**- Affiliation: Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, E-30203 Cartagena, Murcia, Spain
- MR Author ID: 692410
- Email: pablo.mira@upct.es
- Received by editor(s): May 15, 2007
- Published electronically: June 22, 2009
- Additional Notes: The first author was partially supported by MEC-FEDER Grant No. MTM2007-64504 and Regional J. Andalucia Grants P06-FQM-01642 and FQM 325

The second author was partially supported by MEC-FEDER, Grant No. MTM2007-65249 and the Programme in Support of Excellence Groups of Murcia, by Fund. Seneca, reference 04540/GERM/OG - © Copyright 2009 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**361**(2009), 5737-5752 - MSC (2000): Primary 53A10
- DOI: https://doi.org/10.1090/S0002-9947-09-04645-5
- MathSciNet review: 2529912