Involutory automorphisms of plane convex sets (Q1304984)

A bijection \(s\) of a compact convex set \(K\) in the real affine plane with \(s^2=id\) is called a reflection of \(K\) if \(s\) maps segments onto segments. It is shown that \(K\) is bounded by an ellipse if there are enough reflections with centers on a support line or on a secant of \(K\). Also group theoretical conditions are supposed. Essential for the proofs is that the reflections of \(K\) may be continued to collineations of the real projective plane.