Conformal and holomorphic barycenters in hyperbolic balls
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912131522232320 |
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| author | Jacimovic, Vladimir Kalaj, David |
| author_facet | Jacimovic, Vladimir Kalaj, David |
| contents | We introduce the notions of \textit{conformal barycenter} and \textit{holomorphic barycenter} of a measurable set $D$ in the hyperbolic ball. The two barycenters coincide in the disk, but they differ in multidimensional balls $\mathbb{C}^m \cong \mathbb{R}^{2m}$. These notions are counterparts of barycenters of measures on spheres, introduced by Douady and Earle in 1986. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02257 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal and holomorphic barycenters in hyperbolic balls Jacimovic, Vladimir Kalaj, David Differential Geometry We introduce the notions of \textit{conformal barycenter} and \textit{holomorphic barycenter} of a measurable set $D$ in the hyperbolic ball. The two barycenters coincide in the disk, but they differ in multidimensional balls $\mathbb{C}^m \cong \mathbb{R}^{2m}$. These notions are counterparts of barycenters of measures on spheres, introduced by Douady and Earle in 1986. |
| title | Conformal and holomorphic barycenters in hyperbolic balls |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.02257 |