Stationary discs and finite jet determination for non-degenerate generic real submanifolds

TL;DR

This paper constructs stationary discs for Levi non-degenerate real submanifolds and uses them to achieve 2-jet determination of CR automorphisms under certain conditions.

Contribution

It introduces a method to construct stationary discs for Levi non-degenerate submanifolds and applies this to determine CR automorphisms uniquely by their 2-jets.

Findings

Construction of stationary discs for Levi non-degenerate manifolds

Establishment of 2-jet determination of CR automorphisms

Extension of stationary disc methods to broader non-degeneracy conditions

Abstract

In case M is Levi non-degenerate in the sense Tumanov, we construct stationary discs for $M$. If furthermore M satisfies an additional non-degeneracy condition, we apply the method of stationary discs to obtain 2-jet determination of CR automorphisms of M.