On the Bernstein Problem in the Three-dimensional Heisenberg Group

Canadian mathematical bulletin

Shimpei Kobayashi³  Josef F. Dorfmeister¹  Jun-ichi Inoguchi² 

[1] Fakultät für Mathematik, TU-München, Boltzmann str. 3, D-85747, Garching, Germany;Department of Mathematical Sciences, Faculty of Science, Yamagata University, Yamagata, 990-8560, Japan;Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan

关键词: Bernstein problem;    minimal graphs;    Heisenberg group;    loop groups;    spinors;   

DOI  :  10.4153/CMB-2015-061-3

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this note we present a simple alternative proof for the Bernstein problem in the three-dimensional Heisenberggroup $operatorname{Nil}_3$ by using the loop group technique. We clarify the geometric meaning of the two-parameter ambiguity of entire minimal graphswith prescribed Abresch-Rosenberg differential.

【 授权许可】

Unknown