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Bergman barycentric extensions of boundary homeomorphisms of the complex ball
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 Bergman metric and \(σ_z\) is the visual, equivalently Poisson--Szegő, measure based at \(z\). We prove well-definednes
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