# ApproximatingJ-holomorphic curves by holomorphic ones

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We prove that there are no pseudoholomorphic theories of anything other than curves, even if one allows more general spaces than almost complex manifolds. The proof is elementary, except for theories of pseudoholomorphic hypersurfaces, where topological techniques are needed. Surprisingly,...

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- DISQUES J-HOLOMORPHES CONTENUS. Mazzilli, Emmanuel // Proyecciones - Journal of Mathematics;2009, Vol. 28 Issue 2, p141
We study germs of J-Holomorphic curves contained in M, a real analytic hypersurface of an symplectic manifold of dimension 4. We show, under topological hypothesis on M, that if M is compact then M is of finite type and so there is no germs of J -holomorphic curves on M (with J adapted with the...

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We establish necessary and sufficient conditions for the system of values of a holomorphic vector function to be complete in a FrÃ©chet space. The results obtained are illustrated by several examples.

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We establish necessary and sufficient conditions under which a real-valued function from $$L_p (\mathbb{T})$$ , 1 = p < 8, is badly approximable by the Hardy subspace H := {ï¿½ ? H p : ï¿½(0) = 0}. In a number of cases, we obtain the exact values of the best approximations in the mean of...

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A classical theorem of Valiron states that a function which is holomorphic in the unit disk, unbounded, and bounded on a spiral that accumulates at all points of the unit circle, has asymptotic value $\infty$. This property, and various other properties of such functions, are shown to hold for...