English

Constructions of minimal periodic surfaces and minimal annuli in Sol3

Differential Geometry 2016-01-20 v1

Abstract

We construct two one-parameter families of minimal properly embedded surfaces in the Lie group Sol3 using a Weierstrass-type representation. These surfaces are not invariant by a one-parameter group of ambient isometries. The first one can be viewed as a family of helicoids, and the second one is a family of minimal annuli called catenoids. Finally we study limits of these catenoids, and in particular we show that one of these limits is a new minimal entire graph.

Keywords

Cite

@article{arxiv.1311.5004,
  title  = {Constructions of minimal periodic surfaces and minimal annuli in Sol3},
  author = {Christophe Desmonts},
  journal= {arXiv preprint arXiv:1311.5004},
  year   = {2016}
}

Comments

29 pages