Tobias Ekholm 氏 (University of Uppsala)

Abstract:

A minimal surface in Euclidean space is a surface which is
stationary for the area functional. Examples of such surfaces may
be obtained by dipping wire in soapy water. The total curvature
of a space curve is the total angle its tangent line turns as the
curve is traversed.

In a celebrated paper of 1973, J.C.C Nitsche proved that any
analytic simple closed space curve C of total curvature less than
4\pi bounds a unique minimal disk which is immersed. His analysis
left open the following questions: Is the disk embedded and if C
bounds other minimal surfaces must they also be immersed or in
fact embedded? We shall show that the answer to both these
questions are yes.

The talk is intended for non-specialists.