Unique jet determination of CR maps into Nash sets

Author(s)
Bernhard Lamel, Nordine Mir, Guillaume Rond
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.

Organisation(s)
Faculty of Mathematics, Department of Mathematics
External organisation(s)
Division of Arts and Sciences, Texas A&M University at Qatar, Institut de Mathématiques de Marseille
Journal
Advances in Mathematics
Volume
432
ISSN
0001-8708
DOI
https://doi.org/10.1016/j.aim.2023.109271
Publication date
11-2023
Peer reviewed
Yes
Austrian Fields of Science 2012
101002 Analysis, 101009 Geometry
Keywords
ASJC Scopus subject areas
General Mathematics
Portal url
https://ucrisportal.univie.ac.at/en/publications/9c75109d-f9fb-4e1e-b1fa-846787a6d609