Scientists / Open questions
Jesse Douglas
Minimal surfaces; calculus of variations
1936 Fields Medal
3 questions
Multiplicity of solutions of the classical Plateau problem: uniqueness, finiteness, and the number of minimal surfaces bounded by a given contour
The inverse problem of the calculus of variations for systems of second-order ordinary differential equations in arbitrary dimension (completing the Helmholtz-Douglas solution)
Necessity and minimal regularity hypotheses in Douglas's converse theorem on the diametral locus of an algebraic curve