The uniqueness of the helicoid in the Lorentz-Minkowski space L3
Isabel Fernandez, Francisco J. Lopez
TL;DR
This paper investigates the uniqueness of certain maximal surfaces, specifically the Lorentzian helicoid and Enneper's surface, within the Lorentz-Minkowski space, focusing on those with lightlike boundary and mirror symmetry.
Contribution
It establishes the uniqueness of the Lorentzian helicoid and Enneper's surface among properly embedded maximal surfaces with specific boundary conditions in L3.
Findings
Lorentzian helicoid is unique under given conditions
Enneper's surface shares a similar uniqueness property
Results contribute to the classification of maximal surfaces in Lorentz-Minkowski space
Abstract
In this paper we deal with the uniqueness of the Lorentzian helicoid and Enneper's surface among properly embedded maximal surfaces with lightlike boundary of mirror symmetry in the Lorentz-Minkowski space L3.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds