Levi-flat filling of real two-spheres in symplectic manifolds (II)

TL;DR

This paper proves a result on filling a real two-sphere with a Levi-flat hypersurface within a compact complex manifold with boundary, under certain convexity and symplectic conditions.

Contribution

It establishes conditions under which a real two-sphere with complex points can be filled by a Levi-flat hypersurface in a symplectic manifold.

Findings

Filling of the sphere by a Levi-flat hypersurface is possible under specified conditions.

The result applies to manifolds with smooth Levi convex boundary and tame symplectic form.

The paper extends previous work to include complex points of elliptic and hyperbolic types.

Abstract

We consider a compact complex manifold with smooth Levi convex boundary and a tame symplectic form. Consider a real two-sphere with elliptic and hyperbolic complex points generically embedded to the boundary of manifold. We prove a result on filling of the sphere by a Levi-flat hypersurface.