Smooth solutions to the complex plateau problem

Abstract

The paper builds on work of Du, Gao, and Yau. The main result provides a characterization of smooth solutions, up to normalization, of the complex Plateau problem for strongly pseudoconvex Calabi–Yau CR manifolds of dimension $2n - 1 \geq 5$ and in the hypersurface case when $n = 2$. The latter case was completely solved by Yau for $n \geq 3$ 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.