English

Minimal surfaces in the three dimensional sphere with high symmetry

Geometric Topology 2018-07-06 v2 Differential Geometry

Abstract

Using the Lawson's existence theorem of minimal surfaces and the symmetries of the Hopf fibration, we will construct symmetric embedded closed minimal surfaces in the three dimensional sphere. These surfaces contain the Clifford torus, the Lawson's minimal surfaces, and seven new minimal surfaces with genera 9, 25, 49, 121, 121, 361 and 841. We will also discuss the relation between such surfaces and the maximal extendable group actions on subsurfaces of the three dimensional sphere.

Keywords

Cite

@article{arxiv.1804.05421,
  title  = {Minimal surfaces in the three dimensional sphere with high symmetry},
  author = {Sheng Bai and Chao Wang and Shicheng Wang},
  journal= {arXiv preprint arXiv:1804.05421},
  year   = {2018}
}

Comments

24 pages, 9 figures