Reflection Ideals and mappings between generic submanifolds in complex space
By M. S. Baouendi, Nordine Mir, Linda Preiss Rothschild. 2000
79 citations recorded by the source corpus.
Results on finite determination and convergence of formal mappings between smooth generic submanifolds in ℂN are established in this article. The finite determination result gibes sufficient conditions to guarantee that a formal map is uniquely determined by its jet, of a preassigned order, at a point. Convergence of formal mappings for real-analytic generic submanifolds under appropriate assumptions is proved, and natural geometric conditions are given to assure that if two germs of such submanifolds are formally equivalent, then, they are necessarily biholomorphically equivalent. It is also shown that if two real-algebraic hypersurfaces in ℂN are biholomorphically equivalent, then, they are algebraically equivalent. All the results are first proved in the more general context of “reflection ideals” associated to formal mappings between formal as well as real-analytic and real-algebraic manifolds.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/cf59c17ac03944919cf3423fdfa60151bb12aa54
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Finite jet determination of local analytic CR automorphisms and their parametrization by 2-jets in the finite type case (2001, methodology): “For other results on finite jet determination and finite jet parametrization of local CR automorphisms (in the finite type case), the reader is referred to the papers [H], [BER2,4], [Ha], [L], [ BMR ], [E1], [K], [KZ].”
- Equivalence and embedding problems for CR-structures of any codimension (2001, methodology): “The applications of the Segre sets method include a characterization of the finite type [BER96], unique determination and an (explicit algorithmic) holomorphic parametrization of CR-maps by their jets [BER97, Z97, BER99b, Ki99b, L99b], algebraicity of (real-analytic) CR-maps between real-algebraic C”
- A Bishop surface with a vanishing Bishop invariant (2007, methodology): “In the research described in [BER][ BMR ][MMZ], one tries to understand the convergence of formal CR maps between not too degenerate real analytic CR manifolds.”