The Björling problem for timelike minimal surfaces in \({\mathbb {R}}^{4}_{1}\)

DOI10.1007/s10231-016-0614-3zbMath1427.53004OpenAlexW2538636811MaRDI QIDQ2406437

A. P. Franco Filho, Martha P. Dussan, Martin A. Magid

Publication date: 29 September 2017

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-016-0614-3

zbMATH Keywords

Björling problemsymmetry principlesLorentz-Minkowski spacetime-like surfacesWeierstrass representation formula

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (4)

Timelike surfaces in the de Sitter space \(\mathbb{S}_1^3(1)\subset \mathbb{R}_1^4\) ⋮ Weierstrass representations of Lorentzian minimal surfaces in \(\mathbb{R}^4_2\) ⋮ Spacelike zero mean curvature surfaces in \({\mathbb{L}}^4\) ⋮ Explicit solving of the system of natural PDEs of minimal Lorentz surfaces in \(\mathbb{R}_2^4\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Björling problem for timelike surfaces in \(\mathbb R_2^4\)
• Björling problem for timelike surfaces in the Lorentz-Minkowski space
• Timelike surfaces in Lorentz 3-space with prescribed mean curvature and Gauss map
• Harmonic maps of Lorentz surfaces, quadratic differentials and paraholomorphicity
• A Schwarz-type formula for minimal surfaces in Euclidean space \(\mathbb{R}^n\)
• A Weierstrass representation for minimal surfaces in 3-dimensional manifolds
• A geometric Cauchy problem for timelike minimal surfaces
• On the Björling problem in a three-dimensional Lie group
• The Cauchy problem for the Liouville equation and Bryant surfaces
• The affine Cauchy problem
• Björling problem for space-like, zero mean curvature surfaces in \(\mathbb L^{4}\)
• The Cauchy problem for improper affine spheres and the Hessian one equation
• Björling problem for maximal surfaces in Lorentz–Minkowski space
• A Weierstrass representation theorem for Lorentz surfaces
• The Björling problem for minimal surfaces in a Lorentzian three-dimensional Lie group

This page was built for publication: The Björling problem for timelike minimal surfaces in \({\mathbb {R}}^{4}_{1}\)