Classification of stable minimal surfaces bounded by Jordan curves in close planes in Euclidean three-space.

摘要

In this thesis we study compact stable embedded minimal surfaces whose boundary is given by two collections of closed smooth Jordan curves in two close parallel planes in Euclidean three-space.;Our main result is to give a classification of these minimal surfaces, under certain natural asymptotic geometric constraints, in terms of certain associated varifolds which can be enumerated explicitly.;One consequence of the main theorem is that under our hypotheses, there exists a unique area-minimizing surface, and this surface has the largest possible genus among all stable embedded minimal surfaces with boundary the two families of curves introduced above.