Unique jet determination of CR maps into Nash sets

Bernhard Lamel, Nordine Mir (Corresponding author), Guillaume Rond

Publications: Contribution to journalArticlePeer Reviewed

Abstract

Let M⊂CN be a real-analytic CR submanifold, M⊂CN a Nash set and EM the set of points in M of D'Angelo infinite type. We show that if M is minimal, then, for every point p∈M, and for every pair of germs of C-smooth CR maps f,g:(M,p)→M, there exists an integer k=kp such that if f and g have the same k-jets at p, and do not send M into EM, then necessarily f=g. Furthermore, the map p↦kp may be chosen to be bounded on compact subsets of M. As a consequence, we derive the finite jet determination property for pairs of germs of CR maps from minimal real-analytic CR submanifolds in CN into Nash subsets in CN of D'Angelo finite type, for arbitrary N,N≥2.

Original languageEnglish
Article number109271
JournalAdvances in Mathematics
Volume432
DOIs
Publication statusPublished - 1 Nov 2023

Austrian Fields of Science 2012

  • 101002 Analysis
  • 101009 Geometry

Keywords

  • CR maps
  • Finite jet determination

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