A New Approach for the Circular Inversion in l1- Normed Spaces

Temel Ermiş; Ali Osman Şen; Johan Gielis

doi:10.20944/preprints202405.1453.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 22 May 2024 / Approved: 22 May 2024 / Online: 22 May 2024 (15:12:02 CEST)

While there are well-known synthetic methods in the literature to find the image of a point under circular inversion in l2−normed geometry (Euclidean geometry), there is no similar synthetic method in Minkowski geometry, also known as the geometry of finite-dimensional Banach spaces. In this study, we have succeeded in giving a synthetic construction for the circular inversion in l1−normed spaces, which is one of the most fundamental examples of Minkowski geometry. Moreover, this synthetic construction has been given using the Euclidean circle, independently of the l1−norm.

Finite-Dimensional Banach Spaces; Minkowski Geometry; Metric Geometry; l1-Norm; Manhattan Metric, Taxicab Metric

Computer Science and Mathematics, Geometry and Topology

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A New Approach for the Circular Inversion in l1- Normed Spaces

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