Members & Former Members

M. Sc. Penelope Gehring

Doctoral student

Project

37Boundary value problems and index theory on Riemannian and Lorentzian manifolds

Publications within SPP2026

Non-local boundary conditions, such as the Atiyah-Patodi-Singer (APS) conditions, for Dirac operators on Riemannian manifolds are well under\-stood while not much is known for such operators on spacetimes with timelike boundary. We define a class of Lorentzian boundary conditions that are local in time and non-local in the spatial directions and show that they lead to a well-posed Cauchy problem for the Dirac operator. This applies in particular to the APS conditions imposed on each level set of a given Cauchy temporal function.

 

 

Related project(s):
37Boundary value problems and index theory on Riemannian and Lorentzian manifolds

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