On the affine heat equation for non-convex curves

In this paper, we extend to the non-convex case theaffine invariant geometric heat equationstudied by Sapiro and Tannenbaum for convex plane curves. We prove that a smooth embedded plane curve will converge to a point when evolving according to this flow. This result extends the analogy between the affine heat equation and the well-knownEuclidean geometric heat equation.