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Singular Miminal Ruled Surfaces

Published 10 Aug 2023 in math.DG | (2308.05499v1)

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 $\alpha-$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 $3-$space.

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