What type of study is this?

This is a Quantitative Study study (also classified as: Experimental Study).

October 16, 2025Open Access

Hilbert metric and quasiconformal mappings

Puntos clave

A functional identity relates the hilbert metric and visual angle metric, improving our understanding of metric relationships.
Sharp distortion results for quasiregular mappings and analytic functions are derived from the hilbert metric and visual angle metric.
The study shows that hilbert circles correspond to euclidean ellipses, revealing new geometric insights.
Computer algebra methods, specifically gröbner bases, were instrumental in the proofs and findings.

Resumen

We prove a functional identity between the Hilbert metric and the visual angle metric in the unit disk. The proof utilizes the Poincar\'e hyperbolic metric in terms of which both metrics can be expressed. This identity then yields sharp distortion results for quasiregular mappings and analytic functions, expressed in terms of the Hilbert metric. We also prove that Hilbert circles are, in fact, Euclidean ellipses. The proof makes use of computer algebra methods. In particular, Gr\"obner bases are used.

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