It allows mathematicians to extend tools from differential geometry to a much larger class of surfaces that are not necessarily smooth.
It was solved independently in the 1930s by Jesse Douglas and Tibor Radó under certain topological restrictions.
In 1960 Herbert Federer and Wendell Fleming used the theory of currents with which they were able to solve the orientable Plateau's problem analytically without topological restrictions, thus sparking geometric measure theory.
Later Jean Taylor after Fred Almgren proved Plateau's laws for the kind of singularities that can occur in these more general soap films and soap bubbles clusters.
The following objects are central in geometric measure theory: The following theorems and concepts are also central: The Brunn–Minkowski inequality for the n-dimensional volumes of convex bodies K and L, can be proved on a single page and quickly yields the classical isoperimetric inequality.