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

• Autorzy: Daniel Barlet , Teresa Monteiro Fernandes
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 32B20: Semi-analytic sets and subanalytic sets
• 32C09: Embedding of real analytic manifolds
• 32C05: Real-analytic manifolds, real-analytic spaces
• 14P15: Real analytic and semianalytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 204
• Numer: 3
• Strony: 265-274

Daty

wydano

2011

Twórcy

autor

Daniel Barlet

• Institut Élie Cartan, Université de Nancy, Laboratoire de Mathématiques, B.P. 239, 54506 Vandœuvre-lès-Nancy Cedex, France

autor

Teresa Monteiro Fernandes

• Centro de Matemática e Aplicações Fundamentais, Departamento de Matemática, da Faculdade de Ciências, da Universidade de Lisboa, Edifício C6, P.2, Campo Grande, 1749-16 Lisboa, Portugal

Identyfikatory

DOI

10.4064/sm204-3-5