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