Conformal and holomorphic barycenters in hyperbolic balls
Abstract
We introduce the notions of conformal barycenter and holomorphic barycenter of a measurable set D in the hyperbolic ball. The two barycenters coincide in the disk, but they differ in multidimensional balls Cm R2m. These notions are counterparts of barycenters of measures on spheres, introduced by Douady and Earle in 1986.
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