Local geometric properties of real submanifolds in complex space

DOI10.1090/S0273-0979-00-00863-6zbMath0955.32027MaRDI QIDQ4955881

Linda Preiss Rothschild, Mohamed Salah Baouendi, P. Ebenfeldt

Publication date: 22 May 2000

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

surveyCR-manifoldscomplex spaceformal equivalencealgebraic equivalencelocal biholomorphic equivalencereal submanifoldsCR-mappings

Mathematics Subject Classification ID

Real submanifolds in complex manifolds (32V40) Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) CR manifolds as boundaries of domains (32V15) Extension of functions and other analytic objects from CR manifolds (32V25) Finite-type conditions on CR manifolds (32V35) Strongly pseudoconvex domains (32T15)

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Cites Work

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• Normal forms for real surfaces in \(C^ 2\) near tangents and hyperbolic surface transformations
• Local characterization of holomorphic automorphisms of Siegel domains
• On the analyticity of CR mappings
• Pseudo holomorphic curves in symplectic manifolds
• Extending proper holomorphic mappings of positive codimension
• Proper holomorphic mappings between real-analytic pseudoconvex domains in \({\mathbb{C}}^ n\)
• Global holomorphic extension of a local map and a Riemann mapping theorem for algebraic domains
• Normal form and two-dimensional chains of an elliptic CR manifold in \(\mathbb{C}^4\)
• On the pseudo-conformal geometry of hypersurface of the space of \(n\) complex variables
• Biholomorphic mappings and the \(\overline\partial\)-problem
• A reflection principle for degenerate real hypersurfaces
• Segre families and real hypersurfaces
• Real hypersurfaces, orders of contact, and applications
• The local hull of holomorphy of a surface in the space of two complex variables
• A construction of normal forms for weakly pseudoconvex CR manifolds in \(C^ 2\).
• Mappings of quadric Cauchy-Riemann manifolds
• On `type' conditions for generic real submanifolds of \(\mathbb{C}^n\)
• Spherical hypersurfaces in complex manifolds
• Pseudoconvex domains with real-analytic boundary
• Deformations of strictly pseudoconvex domains
• CR automorphisms of real analytic manifolds in complex space
• The normal form of germs of four-dimensional real submanifolds in \(\mathbb{C}^5\) at generic \(\mathbb{R}\mathbb{C}\)-singular points
• Parametrization of local biholomorphisms of real analytic hypersurfaces
• Domains with non-compact automorphism group: a survey
• On CR mappings of real quadric manifolds
• On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions
• The equivalence problem for higher-codimensional CR structures
• Complete differential system for the mappings of CR manifolds of nondegenerate Levi forms
• Germs of local automorphisms of real-analytic CR structures and analytic dependence on \(k\)-jets
• On the unique continuation problem for CR mappings into nonminimal hypersurfaces
• Equivalences of real submanifolds in complex space.
• Rational dependence of smooth and analytic CR mappings on their jets
• Example of a real-analytic hypersurface with nonlinearizable stability group
• Deformation of complex structures, estimates for the (partial d) equation, and stability of the Bergman kernel
• The Bergman kernel and biholomorphic mappings of pseudoconvex domains
• On a problem of Moser
• Regularity of CR mappings between algebraic hypersurfaces
• Holomorphic mappings from the ball and polydisc
• Differentiable manifolds in complex Euclidean space
• On generalized graded Lie algebras and geometric structures. I
• Boundary behavior of \(\bar \partial\) on weakly pseudo-convex manifolds of dimension two
• On the Riemann mapping theorem
• On the Reflection Principle in Several Complex Variables
• Envelopes of Holomorphy of Certain 2-Spheres in C 2*
• Analytic surfaces in C^2 and their local hull of holomorphy
• On the Envelope of Holomorphy of a 2-Sphere in ℂ 2
• A Normal Form for Rigid Hypersurfaces in C 2
• Domains in C^2 with noncompact automorphism groups
• INVARIANTS OF ELLIPTIC AND HYPERBOLIC CR-STRUCTURES OF CODIMENSION 2
• Divergence for the normalization of real analytic glancinghypersurfaces
• Schwarz reflection principle in complex spaces of dimension two
• On an 𝑛-manifold in 𝐂ⁿ near an elliptic complex tangent
• Convergence and finite determination of formal CR mappings
• Infinitesimal CR Automorphisms of Rigid Hypersurfaces
• Infinitesimal CR Automorphisms of Real Hypersurfaces
• On 𝐶𝑅-mappings between algebraic Cauchy-Riemann manifolds and separate algebraicity for holomorphic functions
• Proper holomorphic maps in dimension 2 extend
• Several Complex Variables and the Geometry of Real Hypersurfaces
• Boundary regularity of proper holomorphic mappings