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

Florian Bertrand; Francine Meylan

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arXiv · 2112.12176

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

Florian Bertrand·Francine Meylan

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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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Florian Bertrand, Francine Meylan. 2021-12-22. The 1-jet determination of stationary discs attached to generic CR submanifolds. https://arxiv.org/abs/2112.12176

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