The 1-jet determination of stationary discs attached to generic CR submanifolds

2021/12/22 by Florian Bertrand, Bertrand, Florian, Francine Meylan +1 · 1 citation
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2112.12176

openalex publication_date 2021/12/22 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

The existence of a nondefective stationary disc attached to a nondegenerate model quadric in C^N is a necessary condition to ensure the unique 1-jet determination of the lifts of a key family of stationary discs. In this paper, we give an elementary proof of the equivalence when the model quadric is strongly pseudoconvex, recovering a result of Tumanov. Our proof is based on the explicit expression of stationary discs, and opens up a conjecture for the unique 1-jet determination to hold when the model is not necessarily strongly pseudoconvex.

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• New examples of CR submanifolds for the 2-jet determination problem

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