Self-intersection points in classical area-minimizing surfaces

Abstract

In this paper we study the structure at a point of tangential self-intersection in an area-minimizing classical minimal surface inR ⁿ. The result is that the lowest order homogeneous term in the splitting function, i.e. the difference of the height functions from the tangent plane, has the form

$$p(z) = az^k + \bar a\bar z^k , with a \cdot a = 0.$$