PROPERLY EMBEDDED MINIMAL ANNULI BOUNDED BY A CONVEX CURVE

Joaquin Pérez, Antonio Ros
2002 Journal of the Institute of Mathematics of Jussieu  
We prove that given a convex Jordan curve Γ ⊂ {x 3 = 0}, the space of properly embedded minimal annuli in the halfspace {x 3 ≥ 0}, with boundary Γ is diffeomorphic to the interval [0, ∞). Moreover, for a fixed positive number a, the exterior Plateau problem that consists of finding a properly embedded minimal annulus in the upper halfspace, with finite total curvature, boundary Γ and a catenoid type end with logarithmic growth a has exactly zero, one or two solutions, each one with a different
more » ... tability character for the Jacobi operator. Mathematics Subject Classification: Primary 53A10, Secondary 49Q05, 53C42.
doi:10.1017/s1474748002000075 fatcat:ybxjnh7xw5cgrddsea5lt7yhvi