The finite jet determination problem for CR maps of positive codimension into Nash manifolds

Author(s)
Bernhard Lamel, Nordine Mir
Abstract

We prove the first general finite jet determination result in positive codimension for CR maps from real-analytic minimal submanifolds (Formula presented.) into Nash (real) submanifolds (Formula presented.). For a sheaf (Formula presented.) of (Formula presented.) -smooth CR maps from (Formula presented.) into (Formula presented.), we show that the non-existence of so-called 2-approximate CR (Formula presented.) -deformations from (Formula presented.) into (Formula presented.) implies the following strong finite jet determination property: There exists a map (Formula presented.), bounded on compact subsets of (Formula presented.), such that for every point (Formula presented.), whenever (Formula presented.) are two elements of (Formula presented.) with (Formula presented.), then (Formula presented.). Applying the deformation point of view allows a unified treatment of a number of classes of target manifolds, which includes, among others, strictly pseudoconvex, Levi–non-degenerate, but also some particularly important Levi-degenerate targets, such as boundaries of classical domains.

Organisation(s)
Faculty of Mathematics, Department of Mathematics
External organisation(s)
Science Program, Texas A&M University at Qatar
Journal
Proceedings of the London Mathematical Society
Volume
124
Pages
737-771
No. of pages
35
ISSN
0024-6115
DOI
https://doi.org/10.1112/plms.12439
Publication date
06-2022
Peer reviewed
Yes
Austrian Fields of Science 2012
101002 Analysis, 101009 Geometry
ASJC Scopus subject areas
General Mathematics
Portal url
https://ucrisportal.univie.ac.at/en/publications/83cb46a2-ba37-466a-a189-4dce476fdf35