Ruled singular minimal surfaces

In this paper we study surfaces with minimal potential energy under gravitational forces, called singular minimal surfaces. We prove that a ruled singular minimal surface in a Euclidean 3-space is cylindrical, in particular as an alpha-catenary cylinder by a result of Lopez [Ann. Glob. Anal. Geom. 53 (4) (2018) 521-541]. This result is also extended in Lorentz-Minkowski 3-space.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

In this paper, we study surfaces with minimal potential energy under gravitational forces, which are called singular minimal surfaces. We prove that a ruled singular minimal surface in a Euclidean 3-space is cylindrical, specifically an alpha-catenary cylinder, based on a result by Lopez. This result is also extended to Lorentz-Minkowski 3-space.