On the Number of Solutions of Asymptotic Plateau Problem

abstract: We give a simple topological argument to show that the number of solutions of the asymptotic Plateau problem in hyperbolic space is generically unique. In particular, we show that the space of codimension-1 closed submanifolds of sphere at infinity, which bounds a unique absolutely area minimizing hypersurface in hyperbolic n-space, is generic in the space of all codimension-1 closed submanifolds at infinity.