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Rigidity for proper holomorphic ball maps with degenerate CR Gauss map
Abstract
Let n and N be integers with 2≤ n<N, and let F:𝔹n→𝔹N be a proper holomorphic map that admits a CN−n+1-smooth extension to the boundary. We prove that if the CR Gauss map of its boundary restriction is generically degenerate, then F is holomorphically equivalent, under composition with automorphisms of the source and target balls, to Vm⊕ 0 for some positive integer m, where $ V_m(z)=\big(\sqrt{\frac{m!}{α!}} z^α\big)_{|α|=m} $ is the degree-m Veronese map. This resolves a problem posed by Xiaojun Huang.
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BibTeX
@misc{hu2026rigidity,
title = {{Rigidity for proper holomorphic ball maps with degenerate CR Gauss map}},
author = {Tianzhi Hu and Wanke Yin and Pingsan Yuan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06219},
eprint = {2610.06219},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06219},
}
RIS
TY - UNPB
TI - Rigidity for proper holomorphic ball maps with degenerate CR Gauss map
AU - Tianzhi Hu
AU - Wanke Yin
AU - Pingsan Yuan
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06219
UR - https://arxiv.org/abs/2610.06219
AB - Let n and N be integers with 2≤ n<N, and let F:𝔹^n→𝔹^N be a proper holomorphic map that admits a C^N−n+1-smooth extension to the boundary. We prove that if the CR Gauss map of its boundary restriction is generically degenerate, then F is holomorphically equivalent, under composition with automorphisms of the source and target balls, to V_m⊕ 0 for some positive integer m, where $ V_m(z)=\big(\sqrt{\frac{m!}{α!}} z^α\big)_{|α|=m} $ is the degree-m Veronese map. This resolves a problem posed by Xiaojun Huang.
ER -