In this talk we will speak about a forgotten proof due to René Garnier (1928) of Plateau problem in the 3 dimensional euclidean space, in the case of polygonal boundary. The proof is based on the fact that we can associate a Fuchsian equation to any minimal surface bounded by a polygon. The monodromy of the equation is given by the directions of the edges of the polygon. To solve Plateau problem, we are thus led to solve a Riemann-Hilbert problem and to construct isomonodromic deformations. In the case of a quadrilateral boundary, this deformations are given by the Painlevé VI equation.