Stable branched minimal immersions with prescribed boundary
L. M. Simon, Neshan Wickramasekera · Journal of Differential Geometry · 2007
We describe a method for producing smooth 2-valued minimal graphs over the cylindrical region (D \{0})×R n-2 , where D is the disk in R 2 , subject to given continuous 2-valued boundary data on ∂D × R n-2 .Subject to appropriate symmetry assumptions, the construction produces branched minimal immersions in D × R n-2 × R with prescribed boundary and branching at every point of {0} × R n-2 , and we also discuss the nature of the possible singularities along {0} × R n-2 in case of general boundary data.