Proper holomorphic maps from the unit disk to some unit ball

DOI10.1090/proc/13425zbMath1366.32007arXiv1608.02885OpenAlexW2511202895MaRDI QIDQ2970080

Ming Xiao, John P. D'Angelo, Zhenghui Huo

Publication date: 27 March 2017

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

Full work available at URL: https://arxiv.org/abs/1608.02885

zbMATH Keywords

proper holomorphic mappingsunit diskunit ballunitary equivalence, homotopy equivalence

Mathematics Subject Classification ID

Proper holomorphic mappings, finiteness theorems (32H35) Complex spaces with a group of automorphisms (32M99) Function theory on the disc (30J99) Orthogonal and unitary groups in metric geometry (51F25)

Related Items (2)

Holomorphic isometries between products of complex unit balls ⋮ Homotopic equivalence of rational proper holomorphic discs of bounded symmetric domains of type I

Cites Work

• Normal forms, Hermitian operators, and CR maps of spheres and hyperquadrics
• Homotopy equivalence for proper holomorphic mappings
• Boundary behavior of rational proper maps
• Classification of rational holomorphic maps from \(\mathbb{B}^2\) into \(\mathbb{B}^\mathbb{N}\) with degree 2
• Extending proper holomorphic mappings of positive codimension
• On a linearity problem for proper holomorphic maps between balls in complex spaces of different dimensions.
• Holomorphic mappings between hyperquadrics with small signature difference
• On the complexity of proper holomorphic mappings between balls
• The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics
• PROPER HOLOMORPHIC MAPPINGS, POSITIVITY CONDITIONS, AND ISOMETRIC IMBEDDING
• Several Complex Variables and the Geometry of Real Hypersurfaces
• Mapping \(B^n\) into \(B^{2n-1}\)

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