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math.DG2026
Bergman barycentric extensions of boundary homeomorphisms of the complex ball
David Kalaj, Anton Gjokaj, Vladimir Jacimovic
We define a Bergman barycentric extension of boundary homeomorphisms of the complex unit ball by \[ E_B(f)(z)=\barB(f_*σ_z), \] where \(\barB\) is the Busemann barycenter for the B…
math.DG2024
Conformal and holomorphic barycenters in hyperbolic balls
Vladimir Jacimovic, David Kalaj
We introduce the notions of \textit{conformal barycenter} and \textit{holomorphic barycenter} of a measurable set in the hyperbolic ball. The two barycenters coincide in the di…