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

Daniel Barlet, and Teresa Monteiro Fernandes. "Grauert's theorem for subanalytic open sets in real analytic manifolds." Studia Mathematica 204.3 (2011): 265-274. <http://eudml.org/doc/285513>.

@article{DanielBarlet2011,
abstract = {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.},
author = {Daniel Barlet, Teresa Monteiro Fernandes},
journal = {Studia Mathematica},
keywords = {Grauert's theorem; subanalytic sets; Stein open sets},
language = {eng},
number = {3},
pages = {265-274},
title = {Grauert's theorem for subanalytic open sets in real analytic manifolds},
url = {http://eudml.org/doc/285513},
volume = {204},
year = {2011},
}

TY - JOUR
AU - Daniel Barlet
AU - Teresa Monteiro Fernandes
TI - Grauert's theorem for subanalytic open sets in real analytic manifolds
JO - Studia Mathematica
PY - 2011
VL - 204
IS - 3
SP - 265
EP - 274
AB - 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.
LA - eng
KW - Grauert's theorem; subanalytic sets; Stein open sets
UR - http://eudml.org/doc/285513
ER -