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

Abstract

The existence of a non-defective stationary disc attached to a non-degenerate model quadric in CN is a necessary condition to ensure the unique 1-jet determination of the lifts of a key family of stationary discs [6]. In this paper, we give an elementary proof of the equivalence when the model quadric is strongly pseudoconvex, recovering a result of Tumanov [14]. 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. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.