Sheaves and D-modules on Lorentzian manifolds

TL;DR

This paper introduces a new class of causal manifolds including globally hyperbolic spacetimes and proves propagation theorems for sheaves, enabling a global solution to the Cauchy problem for hyperfunction solutions of hyperbolic systems.

Contribution

It defines a broad class of causal manifolds and establishes global propagation theorems, advancing the understanding of sheaves on Lorentzian manifolds.

Findings

Proves global propagation theorems for sheaves on causal manifolds.

Solves the Cauchy problem globally for hyperfunction solutions of hyperbolic systems.

Extends the class of manifolds where hyperbolic PDEs can be globally analyzed.

Abstract

We introduce a class of causal manifolds which contains the globally hyperbolic spacetimes and we prove global propagation theorems for sheaves on such manifolds. As an application, we solve globally the Cauchy problem for hyperfunction solutions of hyperbolic systems.