Principe de Hartogs dans les varie´te´s CR

Let <f>M</f> be a <f>CR</f> manifold. The main results of this paper are the following:<list><list-item><no>(A)</no>When <f>M</f> is real analytic, a semi-global Hartogs extension phenomenon occurs for real analytic <f>CR</f> functions if and only if <f>M</f> is nowhere strictly pseudoconvex and <f>dimRM&ges;3</f>.</list-item><list-item><no>(B)</no>When <f>M</f> is a standard manifold, the Hartogs–Bochner extension phenomenon occurs for non-<f>CR</f>-confined domains if and only if <f>M</f> is nowhere strictly pseudoconvex and <f>dimCRM&ges;2</f>.</list-item><list-item><no>(C)</no>If <f>M</f> is a smooth submanifold of <f>Cn</f> foliated by complex curves, a semi-global Hartogs–Bochner extension phenomenon occurs for smooth non-<f>CR</f>-confined domains if and only if <f>dimCRM&ges;2</f>.</list-item><list-item><no>(D)</no>If <f>M</f> is a real analytic nowhere strictly pseudoconvex manifold and if <f>Ω</f> is a sufficiently small domain in <f>M</f>, a hyperfunction which is real analytic in a neighborhood of <f>bΩ</f> and <f>CR</f> in a neighborhood of <f><ovl type="bar" STYLE="S">Ω</ovl></f> is in fact real analytic on <f>Ω</f>.</list-item></list> [Copyright &y& Elsevier]