Editing Plateau's problem (section)

==History==
Various specialized forms of the problem were solved, but it was only in 1930 that general solutions were found in the context of mappings (immersions) independently by [[Jesse Douglas]] and [[Tibor Radó]].  Their methods were quite different; Radó's work built on the previous work of René Garnier and held only for [[rectifiable curve|rectifiable]] simple closed curves, whereas Douglas used completely new ideas with his result holding for an arbitrary simple closed curve.  Both relied on setting up minimization problems; Douglas minimized the now-named Douglas integral while Radó minimized the "energy".  Douglas went on to be awarded the [[Fields Medal]] in 1936 for his efforts.