Oberflächenrand

Oberflächenrand is the boundary of a surface in the mathematical sense. In topology and differential geometry a surface can be regarded as a two-dimensional manifold, possibly with boundary. The Oberflächenrand ∂S consists of those points that do not have a neighborhood in the surface that is homeomorphic to an open disk, but rather to a half-disk. Points in the interior have disk-shaped neighborhoods. If S is the closed disk in the plane, its Oberflächenrand is the unit circle.

Surfaces with boundary are common in geometry and physics. A surface with boundary is a 2D manifold together with a boundary that is itself a 1D manifold. The boundary components are typically curves; for example, a cylinder has two boundary circles, while a Möbius strip has one boundary component. The concept is essential for defining integrations, orientations, and certain physical models on surfaces that are not closed.

In applied contexts such as computer graphics, finite element modeling, or textile and material science, the Oberflächenrand corresponds to the edges or border of a surface patch or mesh. A closed surface has an empty Oberflächenrand; an open surface has a nonempty Oberflächenrand. The term is the German equivalent of the mathematical boundary of a surface, used to distinguish interior points from edge points.