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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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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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