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 u0 :M →R is a bounded uniformly continuous function, M is a Riemannian manifold, and F : [0,∞) × T ∗M →R. This yields uniqueness of the viscosity solutions of such Hamilton–Jacobi equations. © 2005 Elsevier Inc. All rights reserved