## Explicit Björling Surfaces with Prescribed Geometry

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 $(x(t),y(t))$ one can find a third coordinate $z(t)$ and normal fields $n(t)$ along the space curve $c(t)=(x(t),y(t),z(t))$ so that the Björling formula applied to $c(t)$ and $n(t)$ can be explicitly evaluated. We give many examples.

Publication Date:
2018
Date Submitted:
Jun 28 2019
Pagination:
561--584
Citation:
The Michigan Mathematical Journal
67
3
External Resources: