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- Title
Holomorphic isometric maps from the complex unit ball to reducible bounded symmetric domains.
- Authors
Xiao, Ming
- Abstract
The first part of the paper studies the boundary behavior of holomorphic isometric mappings F = (F 1 , ... , F m) from the complex unit ball 픹 n , n ≥ 2 , to a bounded symmetric domain Ω = Ω 1 × ⋯ × Ω m up to constant conformal factors, where Ω i ′ s are irreducible factors of Ω. We prove every non-constant component F i must map generic boundary points of 픹 n to the boundary of Ω i . In the second part of the paper, we establish a rigidity result for local holomorphic isometric maps from the unit ball to a product of unit balls and Lie balls.
- Subjects
SYMMETRIC domains; UNIT ball (Mathematics); HOLOMORPHIC functions; GEOGRAPHIC boundaries
- Publication
Journal für die Reine und Angewandte Mathematik, 2022, Vol 2022, Issue 789, p187
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/crelle-2022-0029