Finite Propagation Speed for First Order Systems and Huygens' Principle   for Hyperbolic Equations
  We prove that strongly continuous groups generated by first order systems on Riemannian manifolds have finite propagation speed. Our procedure provides a new direct proof for self-adjoint systems, and allows an extension to operators on metric measure spaces. As an application, we present a new approach to the weak Huygens' principle for second order hyperbolic equations. 
Alan McIntosh, Andrew J. Morris
math.AP