surfacefunctional
Surfacefunctional is a term used to denote a functional that assigns a real number to a surface, typically in the context of geometry and the calculus of variations. In mathematical practice, a surface functional F defines a map from a class of surfaces (often embedded or immersed 2-dimensional manifolds in a ambient space such as R^3) to the real numbers, and may depend on the geometry induced by the embedding, such as the metric, curvature, or boundary data. A common way to describe F is through an immersion X: S → M, with the value of the functional determined by geometric quantities computed on the surface S.
Common examples include the area functional A(S) = ∫_S dA, which assigns to each surface its surface
Variational problems for surface functionals seek surfaces that minimize or extremize F under given constraints. The
Applications of surface functionals appear in differential geometry, computer graphics, materials science, and biological membrane modeling,