Current

Summary

An $m$-dimensional current is a continuous linear functional on the smooth compactly supported differential $m$-forms of an open set of $\R^n$. Currents generalise oriented surfaces, in the way that distributions generalise functions. They carry a boundary operator and a notion of mass, and limits of surfaces of bounded area and boundary length exist among them. This makes currents a main tool for the Plateau problem and other minimisation problems in geometric measure theory.