Carathéodory distance-preserving maps between bounded symmetric domains
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917306902249472 |
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| author | Lemmens, Bas Walsh, Cormac |
| author_facet | Lemmens, Bas Walsh, Cormac |
| contents | We study the rigidity of maps between bounded symmetric domains that preserve the Carathéodory/Kobayashi distance. We show that such maps are only possible when the rank of the co-domain is at least as great as that of the domain. When the ranks are equal, and the domain is irreducible, we prove that the map is either holomorphic or antiholomorphic. In the holomorphic case, we show that the map is in fact a triple homomorphism, under the additional assumption that the origin is mapped to the origin. We exploit the large-scale geometry of the Carathéodory distance and use the horocompactification and Gromov product to obtain these results without requiring any smoothness assumptions on the maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08639 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Carathéodory distance-preserving maps between bounded symmetric domains Lemmens, Bas Walsh, Cormac Complex Variables Geometric Topology Metric Geometry 32M15 (Primary) 53C35, 32F45 (Secondary) We study the rigidity of maps between bounded symmetric domains that preserve the Carathéodory/Kobayashi distance. We show that such maps are only possible when the rank of the co-domain is at least as great as that of the domain. When the ranks are equal, and the domain is irreducible, we prove that the map is either holomorphic or antiholomorphic. In the holomorphic case, we show that the map is in fact a triple homomorphism, under the additional assumption that the origin is mapped to the origin. We exploit the large-scale geometry of the Carathéodory distance and use the horocompactification and Gromov product to obtain these results without requiring any smoothness assumptions on the maps. |
| title | Carathéodory distance-preserving maps between bounded symmetric domains |
| topic | Complex Variables Geometric Topology Metric Geometry 32M15 (Primary) 53C35, 32F45 (Secondary) |
| url | https://arxiv.org/abs/2507.08639 |