  We describe a method to show short time uniqueness results for viscosity
solutions of general nonlocal and non-monotone second-order geometric equations
arising in front propagation problems. Our method is based on some lower
gradient bounds for the solution. These estimates are crucial to obtain
regularity properties of the front, which allow to deal with nonlocal terms in
the equations. Applications to short time uniqueness results for the initial
value problems for dislocation type equations, asymptotic equations of a
FitzHugh-Nagumo type system and equations depending on the Lebesgue measure of
the fronts are presented.
