Research Paper#Differential Geometry, Minimal Surfaces, Liouville Equation, Lorentz-Minkowski Space🔬 ResearchAnalyzed: Jan 3, 2026 06:22
Liouville-Weierstrass Correspondence for Minimal Surfaces in Minkowski Space
Analysis
This paper explores a connection between the Liouville equation and the representation of spacelike and timelike minimal surfaces in 3D Lorentz-Minkowski space. It provides a unified approach using complex and paracomplex analysis, offering a deeper understanding of these surfaces and their properties under pseudo-isometries. The work contributes to the field of differential geometry and potentially offers new tools for studying minimal surfaces.
Key Takeaways
- •Unified treatment of spacelike and timelike minimal surfaces.
- •Application of complex and paracomplex analysis.
- •Connection between pseudo-isometries and Möbius-type transformations.
- •Explicit examples of minimal surfaces derived from Liouville equation solutions.
Reference
“The paper establishes a correspondence between solutions of the Liouville equation and the Weierstrass representations of spacelike and timelike minimal surfaces.”