Minkowski Symmetry Sets for 1-Parameter Families of Plane Curves

TL;DR

This paper classifies the generic bifurcations of Minkowski symmetry sets for 1-parameter plane curve families, providing geometric criteria and highlighting differences from Euclidean symmetry sets.

Contribution

It introduces a classification of bifurcations of Minkowski symmetry sets and establishes criteria specific to this geometric context, differing from Euclidean cases.

Findings

Different bifurcation types compared to Euclidean symmetry sets

Geometric criteria for each bifurcation type

Complete classification of generic bifurcations

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 its bitangent pseudo-circles. It is shown that the list of possible bifurcation types are different to those that occur in the list of possible types for the Euclidean symmetry set.