Reflection ideals and mappings between generic submanifolds in complex space

DOI10.1007/BF02930653zbMath1039.32021arXivmath/0012243MaRDI QIDQ1407741

Linda Preiss Rothschild, Nordine Mir, Mohamed Salah Baouendi

Publication date: 21 October 2003

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0012243

zbMATH Keywords

finite determinationbiholomorphically equivalentalgebraically equivalentconvergence of formal mappingssmooth generic submanifolds in \(\mathbb{C}^N\)

Mathematics Subject Classification ID

Real submanifolds in complex manifolds (32V40) Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02)

Related Items (33)

The stationary disc method in the unique jet determination of CR automorphisms ⋮ On nondegeneracy conditions for the Levi map in higher codimension: a survey ⋮ Remarks on the symmetries of a model hypersurface ⋮ Projection on Segre varieties and determination of holomorphic mappings between real submanifolds ⋮ Regularity of continuous CR maps in arbitrary dimension. ⋮ Explicit construction of stationary discs and its consequences for nondegenerate quadrics ⋮ Convergence of formal CR mappings into strongly pseudoconvex Cauchy-Riemann manifolds ⋮ Automorphism groups of minimal real-analytic CR manifolds ⋮ Algebraic approximation in CR geometry ⋮ On some systems of real or complex vector fields and their related Laplacians ⋮ Stationary discs and finite jet determination for non-degenerate generic real submanifolds ⋮ Formal and finite order equivalences ⋮ Finite jet determination of CR mappings ⋮ Divergent CR-equivalences and meromorphic differential equations ⋮ Normal form for infinite type hypersurfaces in \(\mathbb C^2\) with nonvanishing Levi form derivative ⋮ Equivalence problem for Bishop surfaces ⋮ Finite jet determination of CR embeddings ⋮ Linearization of holomorphic germs with quasi-Brjuno fixed points ⋮ Lie group structures on groups of diffeomorphisms and applications to CR manifolds. ⋮ A note on CR mappings of positive codimension ⋮ Determination of formal CR mappings by a finite jet ⋮ Formal versus analytic CR mappings ⋮ Unique jet determination and extension of germs of CR maps into spheres ⋮ Nondefective stationary discs and 2-jet determination in higher codimension ⋮ Explicit bounds for the finite jet determination problem ⋮ Jet determination of smooth CR automorphisms and generalized stationary discs ⋮ Transcendental holomorphic maps between real algebraic manifolds in a complex space ⋮ On formal maps between generic submanifolds in complex space ⋮ Two decades of finite jet determination of CR mappings ⋮ Chern–Moser operators and weighted jet determination problems in higher codimension ⋮ Approximation and convergence properties of formal CR-maps ⋮ Stationary discs for smooth hypersurfaces of finite type and finite jet determination ⋮ Study of the analytic regularity of formal CR reflection mappings

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