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