Singular Miminal Ruled Surfaces

2023/08/10 by Aydin, Muhittin Evren, Kara, Ayla Erdur
#53A10 #53C42 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.05499

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 3-space is cylindrical, in particular as an α-catenary cylinder by a result of López [Ann. Glob. Anal. Geom. 53(4) (2018), 521-541]. This result is also extended in Lorentz-Minkowski 3-space.

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