Displaying similar documents to “Fields of CR meromorphic functions”

On the local meromorphic extension of CR meromorphic mappings

Joël Merker, Egmont Porten (1998)

Annales Polonici Mathematici

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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 → 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 × 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...

Decomposition of CR-manifolds and splitting of CR-maps

Atsushi Hayashimoto, Sung-Yeon Kim, Dmitri Zaitsev (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We show the uniqueness of local and global decompositions of abstract CR-manifolds into direct products of irreducible factors, and a splitting property for their CR-diffeomorphisms into direct products with respect to these decompositions. The assumptions on the manifolds are finite non-degeneracy and finite-type on a dense subset. In the real-analytic case, these are the standard assumptions that appear in many other questions. In the smooth case, the assumptions cannot be weakened...

Complex Plateau problem in non-Kähler manifolds

S. Ivashkovich (1998)

Annales Polonici Mathematici

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We consider the complex Plateau problem for strongly pseudoconvex contours in non-Kähler manifolds. We give a necessary and sufficient condition for the existence of solution in the class of manifolds carrying pluriclosed metric forms and propose a conjecture for the general case.

Some applications of a new integral formula for ∂ ̅ b

Moulay-Youssef Barkatou (1998)

Annales Polonici Mathematici

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Let M be a smooth q-concave CR submanifold of codimension k in ℂ n . We solve locally the ∂ ̅ b -equation on M for (0,r)-forms, 0 ≤ r ≤ q-1 or n-k-q+1 ≤ r ≤ n-k, with sharp interior estimates in Hölder spaces. We prove the optimal regularity of the ∂ ̅ b -operator on (0,q)-forms in the same spaces. We also obtain L p estimates at top degree. We get a jump theorem for (0,r)-forms (r ≤ q-2 or r ≥ n-k-q+1) which are CR on a smooth hypersurface of M. We prove some generalizations of the Hartogs-Bochner-Henkin...

On the removable singularities for meromorphic mappings.

Evgeny M. Chirka (1996)

Publicacions Matemàtiques

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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.