On the compactification of hyperconcave ends and the theorems of Siu-Yau and Nadel

Abstract

We show that the 'pseudoconcave holes' of some naturally arising class of manifolds, called hyperconcave ends, can be filled in, including the case of complex dimension two. As a consequence we obtain a stronger version of the compactification theorem of Siu-Yau and extend Nadel's theorems to dimension two.