ABSTRACT
In [7], problem 21, S.T. Yau described the following problem. Let R be a surface in Euclidean space ℝ3. For each point on a unit sphere S 2 consider a ray from the origin through that point that strikes the surface R and reflects off according to the laws of geometric optics. The direction of the reflected ray defines a point on S 2 and, thus, we have a map from S 2 into S 2. How much information about the surface R is contained in this map?
