On the Asymptotic Plateau Problem in Hyperbolic Space

Abstract

We are concerned with the so-called asymptotic Plateau problem in hyperbolic space. That is, to prove the existence of hypersurfaces in hyperbolic space whose principal curvatures satisfy a general curvature relation and has a precribed asymptotic boundary at infinity. In this thesis, by following the method of Bo Guan, Joel Spruck and their collaborators, we solve the problem with the aid of an additional assumption. In particular, our result applies to hypersurfaces whose principal curvatures lie in the k-th Garding cone and has constant (k,k-1) curvature quotient.