Singular Miminal Ruled Surfaces
Differential Geometry
2023-08-11 v1
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.
Keywords
Cite
@article{arxiv.2308.05499,
title = {Singular Miminal Ruled Surfaces},
author = {Muhittin Evren Aydin and Ayla Erdur Kara},
journal= {arXiv preprint arXiv:2308.05499},
year = {2023}
}