In this paper we formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. Our techniques carry over to surfaces with several boundary contours as well as to unoriented surfaces.
We present a modern approach to the classical problem of Plateau based purely on differential geometric concepts. We not only reprove the classical results of Douglas but also develop a new geometric criterion on a given finite system of disjoint Jordan curves in three-dimension…
Meeks and Pérez present a survey of recent spectacular successes in classical minimal surface theory. The classification of minimal planar domains in three-dimensional Euclidean space provides the focus of the account. The proof of the classification depends on the work of many …
