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

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-Süss theorem on the existence of antipodal pairs of a convex curve.

15 pages, 13 figures. The main part of this preprint was previously Section 3 and the part of Section 2 in arXiv:1605.05361v3