Stationary discs and finite jet determination for CR mappings in higher codimension

TL;DR

This paper investigates stationary discs on generic CR manifolds and demonstrates that CR diffeomorphisms are uniquely determined by their 2-jet at a point, using the existence of non-defective stationary discs.

Contribution

It establishes finite jet determination for CR mappings in higher codimension using stationary discs, a novel approach in CR geometry.

Findings

CR diffeomorphisms are uniquely determined by 2-jet at a point

Existence of non-defective stationary discs is proven

Finite jet determination applies to strictly pseudoconvex Levi generating CR manifolds

Abstract

We discuss stationary discs for generic CR manifolds and apply them to the problem of finite jet determination for CR mappings. We prove that a CR diffeomorphism of two finitely smooth strictly pseudoconvex Levi generating CR manifolds is uniquely determined by its 2-jet at a given point. A new key element of the proof is the existence of non-defective stationary discs.