A Weierstrass representation formula for minimal surfaces in \(\mathbb H_{3}\) and \(\mathbb H^{2} \times \mathbb R\)
type: Item
instance of: scholarly article
title: A Weierstrass representation formula for minimal surfaces in \(\mathbb H_{3}\) and \(\mathbb H^{2} \times \mathbb R\)
zbMATH Open document ID: 1119.53041
author: Francesco Mercuri
author: Paola Piu
author: Stefano Montaldo
publication date: 2007-05-24T00:00:00Z
review text: The authors construct a Weierstrass representation for simply connected immersed minimal hypersurfaces in the Heisenberg group \(H_3\) and in \(H^2\times\mathbb R\). They also discuss several examples. This is based on a more general result on harmonic maps and minimal immersions into simply connected Riemannian manifolds.
reviewed by: Linus Kramer
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 5156853
zbMATH Keywords: minimal surfaces
zbMATH Keywords: Weierstrass representation
describes a project that uses: CandS
MaRDI profile type: Publication
full work available at URL: s10114-005-0637-y
OpenAlex ID: W2164973612
cites work: Q3749693
cites work: Q4348477
cites work: Q4274259
cites work: Q4296247
cites work: SO(2)-invariant minimal and constant mean curvature surfaces
cites work: Invariant surfaces of the Heisenberg groups
cites work: Q4516949
cites work: Minimal surfaces in the Heisenberg group
cites work: Minimal surfaces in \(\mathbb{H}^2\times\mathbb{R}\).
cites work: Weierstrass representation for minimal surfaces in hyperbolic space
cites work: Sur certaines structures fibrées complexes
cites work: Harmonic Mappings of Riemannian Manifolds
cites work: Q3662316
cites work: Q4951579
cites work: Minimal surfaces in \(M^2\times \mathbb{R}\)
DOI: 10.1007/S10114-005-0637-Y
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5156853