Plateau’s problem for infinite contours - Tomi, Friedrich (Analysis, 2009)
Plateau’s problem is solved for a certain class of properly embedded unbounded curves in R 3 , i. e. the existence of simply connected properly immersed minimal surfaces is shown which have a given curve from this class as their boundary. The class of admissible boundary contours includes all properly embedded piecewise C 1, α curves with polynomial ends. The constructed surfaces have quadratic area growth.