Stationary discs for smooth hypersurfaces of finite type and finite jet determination

TL;DR

This paper constructs a finite-dimensional invariant manifold of holomorphic discs attached to certain smooth pseudoconvex hypersurfaces in ^2, generalizing stationary discs, and uses this to achieve finite jet determination results.

Contribution

It introduces a new class of holomorphic discs determined by finite jets, extending the concept of stationary discs for smooth hypersurfaces of finite type.

Findings

Constructed a finite-dimensional invariant manifold of holomorphic discs.

Discs are determined by finite jets at boundary points.

Centers of discs fill an open set, enabling jet determination.

Abstract

We construct a finitely dimensional invariant manifold of holomorphic discs attached to a certain class of smooth pseudconvex hypersurfaces of finite type in $\C^2$, generalizing the notion of stationary discs. The discs we construct are determined by a finite jet at a given boundary point and their centers fill an open set. As a consequence, we obtain a finite jet determination result for this class of smooth hypersurfaces.