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

Alexander Tumanov

doi:10.1016/j.aim.2020.107254

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

Alexander Tumanov

Mathematics

Research output: Contribution to journal › Article › peer-review

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 C²-smooth CR diffeomorphism of two C⁴-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.

Original language	English (US)
Article number	107254
Journal	Advances in Mathematics
Volume	371
DOIs	https://doi.org/10.1016/j.aim.2020.107254
State	Published - Sep 16 2020

Keywords

CR mapping
Finite jet determination
Stationary disc

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2020.107254

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title = "Stationary discs and finite jet determination for CR mappings in higher codimension",

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 C2-smooth CR diffeomorphism of two C4-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.",

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author = "Alexander Tumanov",

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N2 - 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 C2-smooth CR diffeomorphism of two C4-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.

AB - 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 C2-smooth CR diffeomorphism of two C4-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.

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KW - Finite jet determination

KW - Stationary disc

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

Abstract

Keywords

ASJC Scopus subject areas

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