Marginalfläche

Marginalfläche is a term used in geometry to denote the surface that forms the boundary of a solid object. In everyday and formal language, this boundary is often called the Randfläche or Grenzfläche, but marginalfläche may appear in some texts as an equivalent label for the boundary surface.

Formally, if S is a solid region in three-dimensional Euclidean space, its marginalfläche is the boundary ∂S. Points on ∂S have the property that every neighborhood of the point intersects both the interior S and the exterior complement of S. If ∂S is smooth, it is a two-dimensional smooth manifold. In cases where the boundary is non-smooth or consists of Several pieces (as in polyhedra), the marginalfläche is piecewise smooth but still serves as the separating surface between inside and outside.

The marginalfläche carries geometric information about the object, such as its shape, orientation, and curvature. When integrating over a surface, one computes over the marginalfläche rather than over the interior. Normal vectors to the boundary are defined almost everywhere and point outward, enabling concepts like surface area, flux, and boundary conditions in physical and numerical problems.

Examples include the boundary surface of a sphere, a cube, or a cylinder. In engineering and computer graphics, marginalflächen are essential for rendering, finite element analysis, and simulations that involve interfaces between materials.

See also: Randfläche, Grenzfläche, boundary, surface, manifold with boundary. Etymologically, marginalfläche combines marginal (edge or border) with Fläche (surface), reflecting its role as the edge-forming surface of a body.