Rectifiable Current

The space of currents arising from rectifiable sets by integrating a differential form is called the space of 2-D rectifiable currents. For $C$ a closed bounded rectifiable curve of a number of components in $\Bbb{R}^3$, $C$ bounds a rectifiable current of least Area. The theory of rectifiable currents generalizes to $m$-D surfaces in $\Bbb{R}^n$.

See also Integral Current, Regularity Theorem

References

Morgan, F. ``What is a Surface?'' Amer. Math. Monthly 103, 369-376, 1996.