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Schwarz Reflection Principle, Boundary Regularity and Compactness for $J$ -Complex Curves

Sergey Ivashkovich; Alexandre Sukhov — 2010

Annales de l’institut Fourier

We establish the Schwarz Reflection Principle for $J$ -complex discs attached to a real analytic $J$ -totally real submanifold of an almost complex manifold with real analytic $J$ . We also prove the precise boundary regularity and derive the precise convergence in Gromov compactness theorem in $𝒞^{k, α}$ -classes.

Schwarz-type lemmas for solutions of $\bar{\partial}$ -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.

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Schwarz Reflection Principle, Boundary Regularity and Compactness for J -Complex Curves

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

Schwarz Reflection Principle, Boundary Regularity and Compactness for $J$ -Complex Curves

Schwarz-type lemmas for solutions of $\bar{\partial}$ -inequalities and complete hyperbolicity of almost complex manifolds