Minkowski symmetry sets for 1-parameter families of plane curves

Journal of Singularities
volume 25 (2022), 361-376

Received: 11 January 2021. Received in revised form: 27 June 2022.

DOI: 10.5427/jsing.2022.25q

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Abstract:

In this paper the generic bifurcations of the Minkowski symmetry set for 1-parameter families of plane curves are classified and the necessary and sufficient geometric criteria for each type are given. The Minkowski symmetry set is an analogue of the standard Euclidean symmetry set, and is defined to be the locus of centres of all of its bitangent pseudo-circles. It is shown that the list of possible bifurcation types is different to that of the list of possible types for the Euclidean symmetry set.

Author(s) information:

Graham Reeve