A remark concerning a mechanical characterization of the sphere

Paris Pamfilos
1986 Proceedings of the American Mathematical Society  
It is shown that if a (sufficiently) small ball rolls freely without sliding on a compact surface in such a way that its center moves with constant in magnitude velocity for every initial condition, then the surface must be a sphere.
doi:10.1090/s0002-9939-1986-0826496-1 fatcat:7qpuxyfdrzcstcajms2cimfvzu