Boundary behavior of rational proper maps

DOI10.1215/S0012-7094-90-06004-1zbMath0694.32016OpenAlexW2084482909MaRDI QIDQ909076

Ted J. Suffridge, Joseph A. Cima

Publication date: 1990

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-90-06004-1

zbMATH Keywords

holomorphic extensionproper mapunit ball

Mathematics Subject Classification ID

Continuation of analytic objects in several complex variables (32D15) Proper holomorphic mappings, finiteness theorems (32H35) Global boundary behavior of holomorphic functions of several complex variables (32E35)

Related Items (27)

CR Complexity and Hyperquadric Maps ⋮ Rigidity of CR maps between Shilov boundaries of bounded symmetric domains ⋮ Proper maps which are Lipschitz \(\alpha\) up to the boundary ⋮ Homotopy equivalence for proper holomorphic mappings ⋮ D'Angelo conjecture in the third gap interval ⋮ Complex geometry and dynamical systems. Abstracts from the workshop held September 4--10, 2022 ⋮ On highly degenerate CR maps of spheres ⋮ Hermitian analogues of Hilbert's 17-th problem ⋮ Proper holomorphic maps from the unit disk to some unit ball ⋮ Non-embeddable real algebraic hypersurfaces ⋮ Regularity of mappings into classical domains ⋮ On the HJY Gap Conjecture in CR geometry vs. the SOS Conjecture for polynomials ⋮ On the third gap for proper holomorphic maps between balls ⋮ CR submanifolds in a sphere and their Gauss maps ⋮ Super-rigidity for CR embeddings of real hypersurfaces into hyperquadrics ⋮ Symmetries in CR complexity theory ⋮ Rational proper holomorphic maps from \(\mathbf B^n\) into \(\mathbf B^{2n}\) ⋮ Holomorphic maps from the complex unit ball to Type IV classical domains ⋮ Degree of a holomorphic map between unit balls from $\mathbb C^2$ to $\mathbb C^n$ ⋮ Unique jet determination and extension of germs of CR maps into spheres ⋮ The CR immersion into a sphere with the degenerate CR Gauss map ⋮ Spherical space forms, CR-mappings, and proper maps between balls ⋮ Proper Holomorphic Maps Between Bounded Symmetric Domains ⋮ Holomorphic extension of meromorphic mappings along real analytic hypersurfaces ⋮ On CR maps from the sphere into the tube over the future light cone ⋮ Rigidity of mappings between degenerate and indefinite hyperbolic spaces ⋮ Rigidity of proper holomorphic maps between bounded symmetric domains

Cites Work

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• A reflection principle with applications to proper holomorphic mappings
• Applications holomorphes propres continues de domaines strictement pseudoconvexes de \({\mathbb{C}}^ n\) dans la boule unité de \({\mathbb{C}}^{n+1}\). (On the extension of proper holomorphic mappings from strictly pseudoconvex domains in \({\mathbb{C}}^ n\) into the unit ball of \({\mathbb{C}}^{n+1})\)
• A reflection principle for proper holomorphic mappings of strongly pseudoconvex domains and applications
• Maps from the two-ball to the three-ball
• Extension of proper holomorphic mappings past the boundary
• Embeddings and proper holomorphic maps of strictly pseudoconvex domains into polydiscs and balls
• Extending proper holomorphic mappings of positive codimension
• Analytic hypoellipticity of the (partial-d-bar)-Neumann problem and extendability of holomorphic mappings
• On mapping an n-ball into an (n+1)-ball in complex space
• Embedding Strictly Pseudoconvex Domains Into Balls

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