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Schwarz-type lemmas for solutions of ¯ -inequalities and complete hyperbolicity of almost complex manifolds

Sergey Ivashkovich, Jean-Pierre Rosay (2004)

Annales de l'Institut Fourier

The definition of the Kobayashi-Royden pseudo-metric for almost complex manifolds is similar to its definition for complex manifolds. We study the question of completeness of some domains for this metric. In particular, we study the completeness of the complement of submanifolds of co-dimension 1 or 2. The paper includes a discussion, with proofs, of basic facts in the theory of pseudo-holomorphic discs.

Some characterizations of hyperbolic almost complex manifolds

Fathi Haggui, Adel Khalfallah (2010)

Annales Polonici Mathematici

First, we give some characterizations of the Kobayashi hyperbolicity of almost complex manifolds. Next, we show that a compact almost complex manifold is hyperbolic if and only if it has the Δ*-extension property. Finally, we investigate extension-convergence theorems for pseudoholomorphic maps with values in pseudoconvex domains.

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