Filling real hypersurfaces by pseudoholomorphic discs

TL;DR

This paper investigates conditions under which pseudoholomorphic discs can fill a neighborhood of a real hypersurface in an almost complex manifold, advancing understanding of their boundary behavior.

Contribution

It provides new sufficient conditions for filling a one-sided neighborhood of a hypersurface with pseudoholomorphic discs.

Findings

Established criteria for filling neighborhoods with discs

Extended understanding of boundary behavior of pseudoholomorphic discs

Contributed to the theory of almost complex manifolds

Abstract

We study pseudoholomorphic discs with boundaries attached to a real hypersurface in an almost complex manifold. We give sufficient conditions for filling a one sided neighborhood of the hypersurface by the discs.