Singular Miminal Ruled Surfaces
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 L\'opez [Ann. Glob. Anal. Geom. 53(4) (2018), 521-541]. This result is also extended in Lorentz-Minkowski 3-space.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.