Componentwise rigidity of holomorphic isometric maps between bounded symmetric domains with negative conformal factors
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Xiao, Ming
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7214056666