On the Compactification of Hyperconcave Ends and the Theorems of Siu -yau and Nadel
نویسنده
چکیده
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.
منابع مشابه
On the Compactification of Concave Ends
The concave end of a 1-corona ρ : X →]a, b[ always can be compactified if n := dimX ≥ 3. This was proved by Rossi [Ro] and Andreotti-Siu [AS]. For n = 2 this not true in general, as shown by a counterexample of Grauert, Andreotti-Siu and Rossi [AS, Gr, Ro]. However, if the concave end of a 1-corona ρ : X →]a, b[ is even hyperconcave (i.e. a = −∞), then this is again true also for dimX = 2. This...
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تاریخ انتشار 2007