Parameterized Plane Curves, Minkowski Caustics, Minkowski Vertices and Conservative Line Fields


Some time ago I made the following observation ([T1]) generalizing the classical 4vertex theorem. Consider a smooth closed strictly convex parameterized curve γ(t) in the oriented affine plane. The acceleration vectors γ (t) (where prime denotes d/dt) generate a smooth line field l(t) along the curve. Assume that these lines rotate in the same sense along… (More)