Holomorphic extension from weakly pseudoconcave CR manifolds

Andrea Altomani; C. Denson Hill; Mauro Nacinovich; Egmont Porten

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Let M be a generic CR submanifold in $ℂ^{m + n}$ , m = CR dim M ≥ 1, n = codim M ≥ 1, d = dim M = 2m + n. A CR meromorphic mapping (in the sense of Harvey-Lawson) is a triple $(f,_{f}, [Γ_{f}])$ , where: 1) $f :_{f} \to Y$ is a ¹-smooth mapping defined over a dense open subset $_{f}$ of M with values in a projective manifold Y; 2) the closure $Γ_{f}$ of its graph in $ℂ^{m + n} \times Y$ defines an oriented scarred ¹-smooth CR manifold of CR dimension m (i.e. CR outside a closed thin set) and 3) $d [Γ_{f}] = 0$ in the sense of currents. We prove that $(f,_{f}, [Γ_{f}])$ extends meromorphically...

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If E is a closed subset of locally finite Hausdorff (2n-2)-measure on an n-dimensional complex manifold Ω and all the points of E are nonremovable for a meromorphic mapping of Ω E into a compact Kähler manifold, then E is a pure (n-1)-dimensional complex analytic subset of Ω.