Explicit Björling Surfaces with Prescribed Geometry

2016/08/18 by López, Rafael, Weber, Matthias
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.05335

Abstract

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.

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