Multipoint Schwarz-Pick Lemma for the quaternionic case
arXiv:2312.09664 · doi:10.1007/s12220-026-02400-5
Abstract
Following ideas by Beardon, Minda and Baribeau, Rivard, Wegert in the context of the complex Schwarz-Pick Lemma, we use iterated hyperbolic difference quotients to prove a quaternionic multipoint Schwarz-Pick Lemma, in the context of the theory of slice regular functions. As applications, we obtain quaternionic Dieudonné and Goluzin estimates. Finally, an algorithm for the construction of (Nevanlinna-Pick) interpolating slice regular functions with real nodes is provided as a byproduct of the quaternionic multipoint Schwarz-Pick Lemma.
To appear in The Journal of Geometric Analysis, final version, 32 pages