TY - JOUR
T1 - Unique jet determination of CR maps into Nash sets
AU - Lamel, Bernhard
AU - Mir, Nordine
AU - Rond, Guillaume
N1 - Publisher Copyright:
© 2023 The Author(s)
PY - 2023/11/1
Y1 - 2023/11/1
N2 - 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.
AB - 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.
KW - CR maps
KW - Finite jet determination
UR - http://www.scopus.com/inward/record.url?scp=85168999173&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2023.109271
DO - 10.1016/j.aim.2023.109271
M3 - Article
AN - SCOPUS:85168999173
SN - 0001-8708
VL - 432
JO - Advances in Mathematics
JF - Advances in Mathematics
M1 - 109271
ER -