Minimal surfaces with non-trivial geometry in the three-dimensional Heisenberg group-Reference-Cited by-同舟云学术

Minimal surfaces with non-trivial geometry in the three-dimensional Heisenberg group

Published:2022-01-01 Issue:1 Volume:9 Page:285-336
ISSN:2300-7443
Container-title:Complex Manifolds
language:en
Short-container-title:

Author:

Dorfmeister Josef F.¹,Inoguchi Jun-ichi²,Kobayashi Shimpei²

Affiliation:

1. Fakultät für Mathematik , TU-München , Boltzmann str. 3, D-85747 , Garching , Germany

2. Department of Mathematics , Hokkaido University , Sapporo , , Japan

Abstract

Abstract We study symmetric minimal surfaces in the three-dimensional Heisenberg group Nil3 using the generalized Weierstrass type representation, the so-called loop group method. In particular, we will present a general scheme for how to construct minimal surfaces in Nil3 with non-trivial geometry. Special emphasis will be put on equivariant minimal surfaces. Moreover, we will classify equivariant minimal surfaces given by one-parameter subgroups of the isometry group Iso◦(Nil3) of Nil3.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/coma-2021-0141/pdf

Reference46 articles.

1. [1] U. Abresch, H. Rosenberg. Generalized Hopf differentials. Mat. Contemp. 28: 1–28, 2005.

2. [2] P. Bérard, M. P. Cavalcante. Stability properties of rotational catenoids in the Heisenberg group. Mat. Contemp. 43: 37–60, 2012.

3. [3] D. A. Berdinski˘ı. Surfaces of constant mean curvature in the Heisenberg group (Russian). Mat. Tr. 13(2): 3–9, 2010. English translation: Siberian Adv. Math. 22(2): 75–79, 2012.

4. [4] D. A. Berdinski˘ı, I. A. Ta˘ımanov. Surfaces in three-dimensional Lie groups (Russian). Sibirsk. Mat. Zh. 46(6): 1248–1264, 2005. English translation: Siberian Math. J. 46(6): 1005–1019.

5. [5] D. Brander, W. Rossman, N. Schmitt. Holomorphic representation of constant mean curvature surfaces in Minkowski space: consequences of non-compactness in loop group methods. Adv. in Math. 223(3): 949–986, 2010.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Minimal cylinders in the three-dimensional Heisenberg group;Mathematische Annalen;2023-03-24