Horofunction compactifications and local Gromov model domains
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908696621088768 |
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| author | Chandel, Vikramjeet Singh Gorai, Sushil Maitra, Anwoy Sarkar, Amar Deep |
| author_facet | Chandel, Vikramjeet Singh Gorai, Sushil Maitra, Anwoy Sarkar, Amar Deep |
| contents | We explore the horofunction compactification of complete hyperbolic domains in complex Euclidean space equipped with the Kobayashi distance. We provide a sufficient condition under which, given a domain $Ω$ as above, the identity map from $Ω$ to itself extends to an embedding of $\overlineΩ$ into the horofunction compactification of $(Ω,k_Ω)$, with $k_Ω$ denoting the Kobayashi distance on $Ω$. Notably, this condition admits unbounded domains that are not Gromov hyperbolic relative to the Kobayashi distance. We also provide a large class of planar hyperbolic domains satisfying the above condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Horofunction compactifications and local Gromov model domains Chandel, Vikramjeet Singh Gorai, Sushil Maitra, Anwoy Sarkar, Amar Deep Complex Variables 32F45, 30C20, 30D40, 53C23 (Primary) 32Q45, 53C22 (Secondary) We explore the horofunction compactification of complete hyperbolic domains in complex Euclidean space equipped with the Kobayashi distance. We provide a sufficient condition under which, given a domain $Ω$ as above, the identity map from $Ω$ to itself extends to an embedding of $\overlineΩ$ into the horofunction compactification of $(Ω,k_Ω)$, with $k_Ω$ denoting the Kobayashi distance on $Ω$. Notably, this condition admits unbounded domains that are not Gromov hyperbolic relative to the Kobayashi distance. We also provide a large class of planar hyperbolic domains satisfying the above condition. |
| title | Horofunction compactifications and local Gromov model domains |
| topic | Complex Variables 32F45, 30C20, 30D40, 53C23 (Primary) 32Q45, 53C22 (Secondary) |
| url | https://arxiv.org/abs/2512.06321 |