Embedding strictly pseudoconvex domains into balls

Forstnerič, Franc

doi:10.1090/S0002-9947-1986-0831203-7

Embedding strictly pseudoconvex domains into balls
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by Franc Forstnerič

Trans. Amer. Math. Soc. 295 (1986), 347-368

DOI: https://doi.org/10.1090/S0002-9947-1986-0831203-7

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Abstract:

Every relatively compact strictly pseudoconvex domain $D$ with ${{\mathbf {C}}^2}$ boundary in a Stein manifold can be embedded as a closed complex submanifold of a finite dimensional ball. However, for each $n \geq 2$ there exist bounded strictly pseudoconvex domains $D$ in ${\mathbb {C}^n}$ with real-analytic boundary such that no proper holomorphic map from $D$ into any finite dimensional ball extends smoothly to $\overline D$.

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