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Componentwise rigidity of holomorphic isometric maps between bounded symmetric domains with negative conformal factors

  • Ming Xiao
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Abstract

Let D be an irreducible bounded symmetric domain of complex dimension at least two. We study local holomorphic maps from D into products of irreducible bounded symmetric domains satisfying a metric identity with positive and negative conformal factors. Under a noncancellation condition on these factors, we prove that every nonconstant component extends to a holomorphic isometric embedding up to a positive integer factor. This proves a componentwise rigidity conjecture formulated by Cheng--Hao--Yuan--Zhang.

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Cite

BibTeXRIS
BibTeX
@misc{xiao2026componentwise,
  title = {{Componentwise rigidity of holomorphic isometric maps between bounded symmetric domains with negative conformal factors}},
  author = {Ming Xiao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.24013},
  eprint = {2609.24013},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24013},
}
RIS
TY  - UNPB
TI  - Componentwise rigidity of holomorphic isometric maps between bounded symmetric domains with negative conformal factors
AU  - Ming Xiao
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.24013
UR  - https://arxiv.org/abs/2609.24013
AB  - Let D be an irreducible bounded symmetric domain of complex dimension at least two. We study local holomorphic maps from D into products of irreducible bounded symmetric domains satisfying a metric identity with positive and negative conformal factors. Under a noncancellation condition on these factors, we prove that every nonconstant component extends to a holomorphic isometric embedding up to a positive integer factor. This proves a componentwise rigidity conjecture formulated by Cheng--Hao--Yuan--Zhang.
ER  -