Hamiltonian flows of curves in and vector soliton equations of mKdV and sine-Gordon type.
Hardy's uncertainty principle, convexity and Schrödinger evolutions
We prove the logarithmic convexity of certain quantities, which measure the quadratic exponential decay at infinity and within two characteristic hyperplanes of solutions of Schrödinger evolutions. As a consequence we obtain some uniqueness results that generalize (a weak form of) Hardy’s version of the uncertainty principle. We also obtain corresponding results for heat evolutions.