On the singular structure of two-dimensional area minimizing surfaces in \({\mathbb{R}}^ n\) (Q800632)

The author investigates which combinations of planes through the origin minimize area and applies this theory to the tangent cone to any area minimizing surface. The main results are: (1) ''A tangent cone to an oriented two-dimensional area minimizing surface in \(R^ n\) consists entirely of complex planes'', (2) ''In some neighbourhood of an interior singular point a, an oriented two-dimensional area minimizing surface in \(R^ n\) consists of at most n/2 manifolds, which intersect orthogonally at a''.