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

2013/07/31 by Florian Bertrand, Bertrand, Florian, Giuseppe Della Sala +1 · 1 citation
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1307.8364

openalex publication_date 2013/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a finitely dimensional invariant manifold of holomorphic discs attached to a certain class of smooth pseudconvex hypersurfaces of finite type in \C², 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.

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• Construction of stationary discs for perturbations of decoupled submanifolds in ℂ⁴

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