PROPERLY EMBEDDED MINIMAL ANNULI BOUNDED BY A CONVEX CURVE

Abstract

We prove that given a convex Jordan curve , the space of properly embedded minimal annuli in the half-space . Moreover, for a fixed positive number , the exterior Plateau problem that consists of finding a properly embedded minimal annulus in the upper half-space, with finite total curvature, boundary has exactly zero, one or two solutions, each one with a different stability character for the Jacobi operator.AMS 2000 Mathematics subject classification: Primary 53A10. Secondary 49Q05; 53C42