The Björling problem for minimal surfaces in a Lorentzian three-dimensional Lie group (Q5964953)

The Björling problem is the problem of determining of a minimal surface passing through a given curve with a prescribed normal field. The aim of the paper under review is to show how the classical Weierstrass representation can be used to establish the existence and the uniqueness of the Björling problem for time-like (resp. space-like) contours in three-dimensional Lie groups. The main idea of the proof is to reduce the original problem to a certain Cauchy-Kovalevskaya type system. Several examples of minimal surfaces in the Heisenberg group \(\mathbb{H}_3\), the de Sitter space \(\mathbb{S}_1^3\), and the product space \(\mathbb{H}^2\times \mathbb R{}\) are also considered.