Conformal and holomorphic barycenters in hyperbolic balls

Vladimir Jacimovic; David Kalaj

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arXiv · 2410.02257

Conformal and holomorphic barycenters in hyperbolic balls

Vladimir Jacimovic·David Kalaj

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Abstract

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.

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BibTeX RIS

Vladimir Jacimovic, David Kalaj. 2024-10-03. Conformal and holomorphic barycenters in hyperbolic balls. https://arxiv.org/abs/2410.02257

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