Classification of Stable Minimal Surfaces Bounded by Jordan Curves in Close Planes

Details Classification of Stable Minimal Surfaces Bounded by Jordan Curves in Close Planes Classification of Stable Minimal Surfaces Bounded by Jordan Curves in Close Planes

1999-05-08

arxiv.org/abs/math/9905047v1

Mathematics

Differential Geometry

38 pages, 2 figures, latex

Scientific paper

We study compact stable embedded minimal surfaces whose boundary is given by two collections of closed smooth Jordan curves in close planes of Euclidean 3-space. Our main result is a classification of these minimal surfaces, under certain natural geometric asymptotic constraints, in terms of certain associated varifolds which can be enumerated explicitely. One consequence of this result is the uniqueness of the area minimizing examples. Another is the asymptotic nonexistence of stable compact embedded minimal surfaces of positive genus bounded by two convex curves in parallel planes.

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