https://neckpinch.com/authors/serge-tabachnikov/New arXiv papers by Serge Tabachnikov, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2112.07852/arxiv:2112.07852Wed, 15 Dec 2021 00:00:00 GMTGil Bor, Serge Tabachnikov — A point source of light is placed inside an oval. The n-th caustic by reflection is the envelope of the light rays emanating from the light source after n reflections off the curve. We show that each of these caustics, for a generic point light source, has at least 4 cusps. This is a billiard variation on Jacobi's Last Geometric Statement, concerning the number of cusps of the conjugate locus of a point on a convex surface. We present various proofs, using different ideas, including the curve shortening flow and Legendrian knot theory.Curve shortening