On the Bernstein Problem in the Three-dimensional Heisenberg Group

• Dorfmeister, Josef F.

• Inoguchi, Jun-ichi

• Kobayashi, Shimpei

Abstract

In this note we present a simple alternative proof for the Bernstein problem in the threedimensional Heisenberg group Nil(3) by using the loop group technique. We clarify the geometric meaning of the two-parameter ambiguity of entire minimal graphs with prescribed AbreschRosenberg differential.

Journal

• Canadian Mathematical Bulletin

  Canadian Mathematical Bulletin 59 (1), 50-61, 2016-03

  Canadian Mathematicla　Society

Keywords

• Bernstein problem
• minimal graphs
• Heisenberg group
• loop groups
• spinors

Details

• CRID: 1050001339019519232
• NII Article ID: 120005756104
• DOI: 10.4153/cmb-2015-061-3
• ISSN: 14964287
• ISSN: 00084395
• HANDLE: 2115/61631
• Web Site: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0008439500019615
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN