Finite jet determination of CR mappings
- Author(s)
- Nordine Mir, Bernhard Lamel
- Abstract
We prove the following finite jet determination result for CR mappings: Given a smooth generic submanifold M ? CN, N = 2, that is essentially finite and of finite type at each of its points, for every point p ? M there exists an integer lp, depending upper-semicontinuously on p, such that for every smooth generic submanifold M' ? CN of the same dimension as M, if h1, h2 : (M, p) ? M' are two germs of smooth finite CR mappings with the same lp jet at p, then necessarily jpk h1 = jpk h2 for all positive integers k. In the hypersurface case, this result provides several new unique jet determination properties for holomorphic mappings at the boundary in the real-analytic case; in particular, it provides the finite jet determination of arbitrary real-analytic CR mappings between real-analytic hypersurfaces in CN of D'Angelo finite type. It also yields a new boundary version of H. Cartan's uniqueness theorem: if O, O' ? CN are two bounded domains with smooth real-analytic boundary, then there exists an integer k, depending only on the boundary ?O, such that if H1, H2 : O ? O' are two proper holomorphic mappings extending smoothly up to ?O near some point p ? ? O and agreeing up to order k at p, then necessarily H1 = H2.
- Organisation(s)
- Department of Mathematics
- External organisation(s)
- Université de Rouen-Normandie
- Journal
- Advances in Mathematics
- Volume
- 216
- Pages
- 153-177
- No. of pages
- 24
- ISSN
- 0001-8708
- Publication date
- 2007
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 1010 Mathematics
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/finite-jet-determination-of-cr-mappings(f4d7ab12-a5a6-4422-9574-e1d32f53a8ea).html