Periodic minimal surfaces in semidirect products

Abstract

In this paper we prove existence of complete minimal surfaces in some metric semidirect products. These surfaces are similar to the doubly and singly periodic Scherk minimal surfaces in ${\mathbb{R}}^3$. In particular, we obtain these surfaces in the Heisenberg space with its canonical metric, and in Sol3 with a one-parameter family of non-isometric metrics.

arXiv commentTo appear in the Journal of the Australian Mathematical Society

Cited by in corpus (2)

• Constructions of minimal periodic surfaces and minimal annuli in Sol3
• The mean curvature equation on semidirect products ${\mathbb{R}}^2{⋊}_A\mathbb{R}$: Height estimates and Scherk-like graphs