Sheaves and D-Modules on Lorentzian Manifolds

  title={Sheaves and D-Modules on Lorentzian Manifolds},
  author={Beno{\^i}t Jubin and P. Schapira},
  journal={Letters in Mathematical Physics},
We introduce a class of causal manifolds which contains the globally hyperbolic spacetimes and prove global propagation theorems for sheaves on such manifolds. As an application, we solve globally the Cauchy problem for hyperfunction solutions of hyperbolic systems. 
A Microlocal Characterization of Lipschitz Continuity
  • Benoît Jubin
  • Mathematics
    Publications of the Research Institute for Mathematical Sciences
  • 2018
We study continuous maps between differential manifolds from a microlocal point of view. In particular, we characterize the Lipschitz continuity of these maps in terms of the microsupport of the
Wick Rotation for D-modules
We extend the classical Wick rotation to D-modules and higher codimensional submanifolds.


Hyperbolic Systems and Propagation on Causal Manifolds
In this paper, which is essentially a survey, we solve the global Cauchy problem on causal manifolds for hyperbolic systems of linear partial differential equations in the framework of
Smoothness of Time Functions and the Metric Splitting of Globally Hyperbolic Spacetimes
The folk questions in Lorentzian Geometry which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic
Compactness of the space of causal curves
We prove that the space of causal curves between compact subsets of a separable globally hyperbolic poset is itself compact in the Vietoris topology. Although this result implies the usual result in
On smooth time functions
  • A. Fathi, A. Siconolfi
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2011
Abstract We are concerned with the existence of smooth time functions on connected time-oriented Lorentzian manifolds. The problem is tackled in a more general abstract setting, namely in a manifold
Global Lorentzian Geometry
Introduction - Riemannian themes in Lorentzian geometry connections and curvature Lorentzian manifolds and causality Lorentzian distance examples of space-times completness and extendibility
A causal order for spacetimes with Lorentzian metrics: proof of compactness of the space of causal curves
We recast the tools of `global causal analysis' in accord with an approach to the subject animated by two distinctive features: a thoroughgoing reliance on order-theoretic concepts, and a utilization
Microlocal theory of sheaves and Tamarkin's non displaceability theorem
This paper is an attempt to better understand Tamarkin's approach of classical non-displaceability theorems of symplectic geometry, based on the microlocal theory of sheaves, a theory whose main
Wave Equations on Lorentzian Manifolds and Quantization
This book provides a detailed introduction to linear wave equations on Lorentzian manifolds (for vector-bundle valued fields). After a collection of preliminary material in the first chapter one
The micro-support of sheaves (see [7]) is a tool to describe local propagation results. A natural problem is then to give sufficient conditions to get global propagation results from the knowledge of
Algebraic approach to Quantum Field Theory
We provide a short introduction to the main features of the algebraic approach to quantum field theories.