Smooth solutions to the complex Plateau problem

Abstract

Building on work of Du, Gao, and Yau, we give a characterization of smooth solutions, up to normalization, of the complex Plateau problem for strongly pseudoconvex Calabi-Yau CR manifolds of dimension 2n − 1 ≥ 5 and in the hypersurface case when n = 2. The latter case was completely solved by Yau for n ≥ 3 but only partially solved by Du and Yau for n = 2. As an application, we determine the existence of a link-theoretic invariant of normal isolated singularities that distinguishes smooth points from singular ones.