A maximum principle for evolution Hamilton–Jacobi equations on Riemannian manifolds

We establish a maximum principle for viscosity subsolutions and supersolutions of equations of the form ut+F(t,dxu)=0, u(0,x)=u0(x), where is a bounded uniformly continuous function, M is a Riemannian manifold, and . This yields uniqueness of the viscosity solutions of such Hamilton–Jacobi equations.