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arXiv · 1511.04578

On a family of pseudohyperbolic disks

Raymond Mortini·Rudolf Rupp
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Abstract

Hyperbolic geometry plays an important role within function theory of the disk. For example, via the Schwarz-Pick Lemma, the isometries of the unit disk $\mathbb D$ with respect to this geometry are the conformal self-maps of $\mathbb D$. In this elementary classroom note, we are interested in the collection of the pseudohyperbolic disks $D_\rho(x,r)$ (with fixed radius $r$ and variable hyperbolic centers $-1<x<1$) and determine explicitely with function theoretic tools the enveloppe of these disks.

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Raymond Mortini, Rudolf Rupp. 2015-11-14. On a family of pseudohyperbolic disks. https://doi.org/10.4171/em%2F290

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