Displaying similar documents to “Hyperbolicity of the Complement of Plane Curves.”

Curves and surfaces in hyperbolic space

Shyuichi Izumiya, Donghe Pei, Masatomo Takahashi (2004)

Banach Center Publications

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In the first part (Sections 2 and 3), we give a survey of the recent results on application of singularity theory for curves and surfaces in hyperbolic space. After that we define the hyperbolic canal surface of a hyperbolic space curve and apply the results of the first part to get some geometric relations between the hyperbolic canal surface and the centre curve.

Normal pseudoholomorphic curves

Fathi Haggui, Adel Khalfallah (2011)

Annales Polonici Mathematici

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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...