Minkowski symmetry sets for 1-parameter families of plane curves

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.