Geometric Wave Equations

Understand

In these lecture notes we discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green operators is discussed including a detailed treatment of the Cauchy problem on a globally hyperbolic manifold both for the smooth and finite order setting.

• As application, the classical Poisson algebra of polynomial functions on the initial values and the dynamical Poisson algebra coming from the wave equation are related.
• The text contains an introduction to the theory of distributions on manifolds as well as detailed proofs.