Maximum principle for viscosity solutions on Riemannian manifolds
  In this work we consider viscosity solutions to second order partial differential equations on Riemannian manifolds. We prove maximum principles for solutions to Dirichlet problem on a compact Riemannian manifold with boundary. Using a different method, we generalize maximum principles of Omori and Yau to a viscosity version. 
Shige Peng and Detang Zhou