Sheaves for spacetimes: a survey
arXiv:2607.14188
summary
The paper surveys how microlocal sheaf‑theoretic methods solve the global Cauchy problem for hyperbolic D‑modules on spacetimes equipped with a time function, using Sato’s hyperfunctions.
Abstract
On a spacetime endowed with a time function (such as a globally hyperbolic manifold) we solve the global Cauchy problem for hyperbolic D-modules in the framework of Sato's hyperfunctions, illustrating the effectiveness of microlocal-sheaf theoretic methods in linear problems.
Topics & keywords
#sheaf theory#hyperbolic equations#D-modules#microlocal analysis#globally hyperbolic spacetimeshyperfunctionsSatoCauchy problemmicrolocal sheaf theoryglobally hyperbolic manifold