25.04.2024, 16:15
– Raum 1.10
Forschungsseminar Differentialgeometrie
Atiyah-Singer-Indexsatz
Lennart Ronge (UP)
Max Lewandowski
We start by discussing under which circumstances a fundamental solution can be restricted to a spacelike Cauchy hypersurface so that the corresponding Cauchy problem is well-posed which will demand some basic microlocal analysis. For the resulting solution we can derive Green's operators and, assuming the wave operator to be formally self-adjoint, prove certain properties of the fundamental solution.