Immobilization of smooth convex figures: Some extensions (Q1375943)

It is known that any plane convex see with \(C^2\) boundary, different from a circular disk, can be immobilized by three points. Here it is shown first that these three points can always be chosen in such a way that a certain curvature condition is fulfilled and secondly that then motion of one of these points forces the other two points to move in a unique way. [On p. 109 \(r-x\) has to be replaced by \(r\cos \theta-x\) and the power series of \(x(\theta)\) starts with \(1- \theta^2/2\). Apparently these corrections do not affect the conclusions].