Geometric Wave Equations

2012/08/23 by Stefan Waldmann, Waldmann, Stefan · 4 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Mathematical and Theoretical Analysis #Nonlinear Waves and Solitons #math-ph #math.AP #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.1208.4706

Updated lecture notes for a lecture held in Freiburg 2008/2009, 279 pages, many figures

arxiv created 2012/08/23 · arxiv updated 2015/03/20

Abstract

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.

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