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

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

2002-10-31

arxiv.org/abs/math/0210485v3

Invent. Math. 164, No. 2, 233-248 (2006)

Mathematics

Complex Variables

13 pages, AMSLaTeX, short version accepted for publication in Inventiones Math

Scientific paper

10.1007/s00222-005-0475-7

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 2 . As a consequence we obtain a stronger version of the
compactification theorem of Siu-Yau and extend Nadel's theorems to dimension 2.

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