Minkowski Symmetry Sets of Plane Curves

We study the Minkowski symmetry set of a closed smooth curveγin the Minkowski plane. We answer the following question, which is analogous to one concerning curves in the Euclidean plane that was treated by Giblin and O’Shea (1990): given a pointponγ, does there exist a bi-tangent pseudo-circle that is tangent toγboth atpand at some other pointqonγ? The answer is yes, but as pseudo-circles with non-zero radii have two branches (connected components) it is possible to refine the above question to the following one: given a pointponγ, does there exist a branch of a pseudo-circle that is tangent toγboth atpand at some other pointqonγ? This question is motivated by the earlier quest of Reeve and Tari (2014) to define the Minkowski Blum medial axis, a counterpart of the Blum medial axis of curves in the Euclidean plane.