Singular Miminal Ruled Surfaces
Muhittin Evren Aydin, Ayla Erdur Kara
TL;DR
This paper investigates singular minimal ruled surfaces in Euclidean and Lorentz-Minkowski 3-space, proving they are cylindrical and extending these results to different geometric contexts.
Contribution
It establishes that singular minimal ruled surfaces are cylindrical in Euclidean space and extends this classification to Lorentz-Minkowski space.
Findings
Singular minimal ruled surfaces are cylindrical in Euclidean 3-space.
Extension of the cylindrical classification to Lorentz-Minkowski 3-space.
Identification of specific types of singular minimal surfaces under gravitational forces.
Abstract
In this paper we study surfaces with minimal potential energy under gravitational forces, called singular minimal surfaces. We prove that a singular minimal ruled surface in a Euclidean space is cylindrical, in particular as an catenary cylinder by a result of L\'{o}pez [Ann. Glob. Anal. Geom. 53(4) (2018), 521-541]. This result is also extended in Lorentz-Minkowski space.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Numerical Analysis Techniques · Computational Geometry and Mesh Generation