Flat Norm

The flat norm on a Current is defined by

$${\mathcal F}(S)=\int\{{\rm Area\ }T+{\rm vol\ }R:S-T=\partial R\},$$

where $\partial R$ is the boundary of $R$.

See also Compactness Theorem, Current

References

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