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Embedding subsets of tori Properly into 2

Erlend Fornæss Wold (2007)

Annales de l’institut Fourier

Let 𝕋 be a complex one-dimensional torus. We prove that all subsets of 𝕋 with finitely many boundary components (none of them being points) embed properly into 2 . We also show that the algebras of analytic functions on certain countably connected subsets of closed Riemann surfaces are doubly generated.

Normal pseudoholomorphic curves

Fathi Haggui, Adel Khalfallah (2011)

Annales Polonici Mathematici

First, we give some characterizations of J-hyperbolic points for almost complex manifolds. We apply these characterizations to show that the hyperbolic embeddedness of an almost complex submanifold follows from relative compactness of certain spaces of continuous extensions of pseudoholomorphic curves defined on the punctured unit disc. Next, we define uniformly normal families of pseudoholomorphic curves. We prove extension-convergence theorems for these families similar to those obtained by Kobayashi,...

On the embedding and compactification of q -complete manifolds

Ionuţ Chiose (2006)

Annales de l’institut Fourier

We characterize intrinsically two classes of manifolds that can be properly embedded into spaces of the form N N - q . The first theorem is a compactification theorem for pseudoconcave manifolds that can be realized as X ¯ ( X ¯ N - q ) where X ¯ N is a projective variety. The second theorem is an embedding theorem for holomorphically convex manifolds into 1 × N .

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