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Grauert's theorem for subanalytic open sets in real analytic manifolds

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Barlet D., Monteiro Fernandes T.

Studia Mathematica

2011

tom 204

nr 3

265-274

By an open neighbourhood in ℂⁿ of an open subset Ω of ℝⁿ we mean an open subset Ω' of ℂⁿ such that ℝⁿ ∩ Ω' = Ω. A well known result of H. Grauert implies that any open subset of ℝⁿ admits a fundamental system of Stein open neighbourhoods in ℂⁿ. Another way to state this property is to say that each open subset of ℝⁿ is Stein. We shall prove a similar result in the subanalytic category: every subanalytic open subset in a paracompact real analytic manifold M admits a fundamental system of subanalytic Stein open neighbourhoods in any complexification of M.

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1 Studia Mathematica

1 Barlet D.

1 Monteiro Fernandes T.

1 2011

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Grauert's theorem for subanalytic open sets in real analytic manifolds