Let P be a set of n points in general position in the plane and consider a set of triangles T={T1,...,Tm} on P. Which sets of triangles have the property that any smooth motion P that preserves the area of all of them extends to a smooth area-preserving motion of the whole plane?
I will give a combinatorial characterization of the generic case of this question and describe an extension to systems of k+1-simplices in k-space.
(Joint work with Ileana Streinu.)