A Weierstrass representation formula for minimal surfaces in \(\mathbb H_{3}\) and \(\mathbb H^{2} \times \mathbb R\)

DOI10.1007/s10114-005-0637-yzbMath1119.53041OpenAlexW2164973612MaRDI QIDQ882715

Francesco Mercuri, Paola Piu, Stefano Montaldo

Publication date: 24 May 2007

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-005-0637-y

zbMATH Keywords

minimal surfacesWeierstrass representation

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

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Minimal surfaces in Lorentzian Heisenberg group and Damek-Ricci spaces via the Weierstrass representation, The Björling problem for prescribed mean curvature surfaces in \(\mathbb{R}^3\), Minimal timelike surfaces in a certain homogeneous Lorentzian 3-manifold, Minimal surfaces in three dimensional Lorentzian Heisenberg group, Enneper representation of minimal surfaces in the three-dimensional Lorentz-Minkowski space, Maximal surfaces in a certain 3-dimensional homogeneous spacetime, A note on minimal surfaces in Euclidean 3-space, A Weierstrass representation for minimal surfaces in 3-dimensional manifolds, Maximal surfaces in Lorentzian Heisenberg space, Complex polynomial vector fields having a finitely curved orbit, Weierstrass representation for surfaces in the three-dimensional Heisenberg group, On the Björling problem in a three-dimensional Lie group, Minimal surfaces in three-dimensional Riemannian manifold associated with a second-order ODE, The Björling problem for minimal surfaces in a Lorentzian three-dimensional Lie group, Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space, Generalized Weierstrass representation for surfaces in Heisenberg spaces

Uses Software

• CandS

Cites Work

• Sur certaines structures fibrées complexes
• Weierstrass representation for minimal surfaces in hyperbolic space
• Minimal surfaces in \(M^2\times \mathbb{R}\)
• Minimal surfaces in \(\mathbb{H}^2\times\mathbb{R}\).
• Invariant surfaces of the Heisenberg groups
• Minimal surfaces in the Heisenberg group
• SO(2)-invariant minimal and constant mean curvature surfaces
• Harmonic Mappings of Riemannian Manifolds
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