Singular points of the Wigner caustic and affine equidistants of planar curves

TL;DR

This paper investigates the singular points of the Wigner caustic and affine equidistants of planar curves, extending classical theorems to understand their geometric properties based on curve shapes.

Contribution

It generalizes the Blaschke-Süss theorem to include the existence of antipodal pairs in convex curves, applied to the study of singularities of affine equidistants.

Findings

Identification of conditions for singular points on Wigner caustic

Extension of classical convex curve theorems

Insights into the geometric structure of affine equidistants

Abstract

In this paper we study singular points of the Wigner caustic and affine $\lambda$--equidistants of planar curves based on shapes of these curves. We generalize the Blaschke-S\"uss theorem on the existence of antipodal pairs of a convex curve.