A short proof of backward uniqueness for some geometric evolution equations

We present a simple, direct proof of the backward uniqueness of solutions to a class of second-order geometric evolution equations which includes the Ricci and cross-curvature flows. The proof, based on a classical argument of Agmon-Nirenberg, uses the logarithmic convexity of a certain energy quantity in the place of Carleman inequalities. We further demonstrate the applicability of the technique to the L2-curvature flow and other higher-order equations.