Weak dispersion for the Dirac equation on asymptotically flat and warped products spaces

TL;DR

This paper establishes local smoothing estimates for the Dirac equation on certain non-flat manifolds, including asymptotically flat and warped product spaces, using the multiplier method.

Contribution

It introduces new local smoothing estimates for the Dirac equation on non-flat geometries, extending previous results to asymptotically flat and warped product spaces.

Findings

Proved local smoothing estimates for the Dirac equation on specific non-flat manifolds.

Extended the applicability of smoothing estimates to asymptotically flat and warped product geometries.

Utilized the multiplier method to achieve these results.

Abstract

We prove local smoothing estimates for the Dirac equation on some non-flat manifolds; in particular, we will consider asymptotically flat and warped products metrics. The strategy of the proofs relies on the multiplier method.