Only ellipsoids have caustics
The author studies the existence problem for the caustics of billiard tables in Euclidean \(d\)-space \(E^d\) for \(d\geq 3\). His main result is that among all convex billiard tables in \(E^d\), \(d\geq 3\), only the solid ellipsoids have convex caustics; The caustics are precisely the confocal solid ellipsoids contained in their interiors and, moreover, the intersection of these. This result settles one conjecture in the author's own paper [Geom. Dedicata 33, 205-226 (1990; Zbl 0696.52001)].
scientific article; zbMATH DE number 840181
scientific article