On the branch point index of minimal surfaces
The authors consider minimal surfaces bounded by smooth Jordan curves (of varying degrees of smoothness). They show that the index of an interior branch point is bounded above by one less than half the maximum number of intersection points of the boundary curve with an affine plane. They observe that the notion of index can be extended to branch points on the boundary if the curve is real analytic by taking an analytic extension of the surface (past the boundary). Furthermore, they give a definition of index for branch points on the boundary even for sufficiently smooth boundary curves under the condition that the curvature and torsion of the boundary curve never vanish and they bound this index above and below. Finally, the authors show that the number of total branch points is finite.
scientific article; zbMATH DE number 5565267