1,348 research outputs found
Schwarz Reflection Principle, Boundary Regularity and Compactness for J-Complex Curves
We establish the Schwarz Reflection Principle for -complex discs attached
to a real analytic -totally real submanifold of an almost complex manifold
with real analytic . We also prove the precise boundary regularity and
derive the precise convergence in Gromov compactness theorem in
\calc^{k,\alpha}-classes.Comment: 21 page
Levi-flat filling of real two-spheres in symplectic manifolds (I)
Let (M,J,w) be a manifold with an almost complex structure J tamed by a
symplectic form w. We suppose that M has complex dimension two, is Levi convex
and has bounded geometry. We prove that a real two-sphere with two elliptic
points, embedded into the boundary of M may be foliated by the boundaries of
pseudoholomorphic discs.Comment: 18 page
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