We develop a new method to construct explicit regular minimal surfaces in Euclidean space that are defined on the entire complex plane with controlled geometry. More precisely, we show that for a large class of planar curves , we can find a third coordinate and normal fields along the space curve so that the Björling formula applied to and can be explicitly evaluated. We give many examples.
"Explicit Björling Surfaces with Prescribed Geometry." Michigan Math. J. 67 (3) 561 - 584, August 2018. https://doi.org/10.1307/mmj/1531447375