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Rigidity for local holomorphic isometric maps from the complex unit ball to reducible bounded symmetric domains
Abstract
Let U be a connected open subset of the complex unit ball Bn, n≥2, and let Fi: U → Ωi be non-constant holomorphic maps into irreducible bounded symmetric domains. We prove that if F=(F1, ⋯, Fm) is a holomorphic isometric map from U to the product of Ωi, then every Fi extends to a proper holomorphic isometric embedding up to a positive constant from Bn into Ωi.
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BibTeX
@misc{yuan2026rigidity,
title = {{Rigidity for local holomorphic isometric maps from the complex unit ball to reducible bounded symmetric domains}},
author = {Yuan Yuan and Xu Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29583},
eprint = {2609.29583},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29583},
}
RIS
TY - UNPB
TI - Rigidity for local holomorphic isometric maps from the complex unit ball to reducible bounded symmetric domains
AU - Yuan Yuan
AU - Xu Zhang
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.29583
UR - https://arxiv.org/abs/2609.29583
AB - Let U be a connected open subset of the complex unit ball B^n, n≥2, and let F_i: U → Ω_i be non-constant holomorphic maps into irreducible bounded symmetric domains. We prove that if F=(F_1, ⋯, F_m) is a holomorphic isometric map from U to the product of Ω_i, then every F_i extends to a proper holomorphic isometric embedding up to a positive constant from B^n into Ω_i.
ER -