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On the Bernstein Problem in the Three-dimensional Heisenberg Group

Published online by Cambridge University Press:  20 November 2018

Josef F. Dorfmeister ,
Jun-ichi Inoguchi  and
Shimpei Kobayashi
Josef F. Dorfmeister
Affiliation:
Fakultät für Mathematik, TU-München, Boltzmann str. 3, D-85747, Garching, Germany e-mail: [email protected]
Jun-ichi Inoguchi
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan e-mail: [email protected]
Shimpei Kobayashi
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan e-mail: [email protected]
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Abstract

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In this note we present a simple alternative proof for the Bernstein problem in the three dimensional Heisenberg group $\text{Ni}{{\text{l}}_{3}}$ by using the loop group technique. We clarify the geometric meaning of the two-parameter ambiguity of entire minimal graphs with prescribed Abresch-Rosenberg differential.

Keywords

53A1053C42Bernstein problemminimal graphsHeisenberg grouploop groupsspinors
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 1 , 01 March 2016 , pp. 50 - 61
Copyright
Copyright © Canadian Mathematical Society 2016

References

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